I'm not a pro mechanic, but I do regularly deal with bikes which are older than the New Millenium. Yes, buying a new master cylinder or a new caliper is probably a safe investment to clear-up your problem.
Ever watch online 'Wheels Through Time', filmed in N. Carolina at the workshop and museum of the same name begun by Dale Walksler and now continued by his son? They regularly acquire some old crock and quickly work through its issues to get it operable: ignition, brakes, fuel system, lighting, and more, to the point they can demonstrate it running up and down the dirt road in-front of their shop. The work may be a prelude to a more comprehensive overhaul of those same parts/systems, but they got it going by working through its issues.
I'll tell you what I suspect is your problem, but first, I would like to know what was involved in your "I have cleaned the master cylinder, as well as the calipers' statement. Did you remove and disassemble the front caliper? It sounds as though you did disassemble and clean the front master cyl and install a rebuild kit. However, this problem continues, what is a path to fix it?
When something isn't performing properly, go back and examine everything you touched. The best way, I've found, is to re-do what I just worked upon.
I would go back and re-do the work. I would install new brake lines, stainless steel jacketed ones, and proceed. I think your brake lines are deteriorating internally. They're shedding the rubber inside the brake line tubing and that rubber is blocking your small port closest to the banjo bolt in the floor of the front brake master cylinder. Replace the brake lines, completely replace the brake fluid and I bet your issue will be fixed.
The brake lines are I suspect the cause of your issue. Also, I suggest disassembly of the caliper. You have a single caliper with 2 pistons, one pair of pistons, where there is one stationary brake pad and one sliding pad. Remove the pistons and thoroughly-clean the caliper, and replace the caliper rubber seals. The brake fluid seal and the dust seal found on each piston are inexpensive. I found Ron Ayres Honda has the seals for $6.87. I use Ron Ayres for Japanese bike parts, they are dealers for the Big Four. I have used them as OEM parts suppliers for decades. If the part is back-ordered, they will send you the part when it becomes available. Their prices are competitive with other online sources.
Use brake fluid to lubricate the rubber seals, make sure the lips of the seals are coated in brake fluid too. Use brake fluid on the pistons and the caliper bores during reassembly. Cleanliness first and always.
Using your new stainless steel jacketed brake lines, reassemble the system. The advantage of the SS lines is the rubber doesn't expand as-much when applying the brake. They make a difference you can feel. I recommend HH grade of brake pads from any reputable brake pad manufacturer. They work in the wet, and when dry too. They don't shed as-much material as organic pads do. That keeps the wheel and fork sliders area cleaner.
I would remove the master cyl and clean it thoroughly, disassembly is needed to do the best job. I know, you said you already did this, do it again to start fresh. Examine the rubbers for any torn/damaged areas. Remember to coat the bore with fresh brake fluid, and to lubricate the rubbers with fresh brake fluid too.
On another forum I participate in, someone had issues with the brake system in the front end, and he found upon disassembly of his newly-installed front brake master cyl rebuild kit, that he had knicked the front brake master cyl piston's rubber seal, causing an internal leakage. That was one of the things I had suggested to him, which could be the problem. Those things can happen, you need to be careful in your work. Fortunately, he found it and didn't resort to throwing wrenches when the issue occurred. He went back to the last work he did, and he found the defective part. What did you last touch in the bike?
Now everything is back together, yes? To fill the brake system, I prefer to do a 'reverse-flush' starting from the caliper bleeder. I use a 60cc irrigation syringe with a 4" piece of 1/4" clear hose on it, slipped onto the irrigation syringe's tapered end. The other end goes onto the caliper bleeder. Open the caliper bleeder and with a filled 60cc irrigation syringe, push the syringe plunger to fill the brake system, from the bottom-up.
Why do it this way? Think of this: what do bubbles do? They float to the surface. You're pushing brake fluid into the system from the caliper bleeder upwards. Any bubbles will migrate up, towards the master cyl. Keep a watch on the master cyl as you empty the syringe. When the syringe is empty, close the bleeder valve. Re-fill the syringe with fresh brake fluid. Again, use the 60cc syringe to fill the brake system. You will see brake fluid appear in the master cyl and along with it, big bubbles and then small bubbles as the brake system fills. Be sure to not have the brake master cyl overflow. You may need to remove some fluid from the master cyl, do it with your handy 60cc syringe, and dispose of it into another container.
You can order a lifetime supply of 60cc (1 mililiter=1 cubic centimeter, or c.c.) irrigation syringes online. It might cost you $10 for 8 of 'em. An irrigation syringe has a tapered tip, making it easy to slip-on a length of 1/4" clear plastic tubing for work on brake caliper bleeders or on hydraulic slave cylinders. There is another type of syringe which is not the same end/tip as the irrigation syringe. That is the Luer-lock syringe, and is commonly used to securely fasten a stainless needle to the syringe. This is not the type of syringe you want.
About filling the master cyl with brake fluid from the caliper bleeder, the position of the handlebar may affect your ability to completely-fill the master cyl. If you have pull-back bars, you may find that the best position is to turn the handlebars all the way to left-lock, positioning the master cyl higher than in a straight-ahead handlebar position. You may find that temporarily loosening the master cyl and rotating it on the handlebar to a level position will give you the best way to fill the master cyl. Just don't forget you didn't put it back in your proper riding position and tighten it!
If you're having to empty brake fluid from the master cyl you are probably ready to try the system. Make sure that the bleeder is tight, the master cyl cap is secure, the master cyl is tight on the bar (see above) and then rapidly pump the brake lever. You should be able to quickly feel the brake lever develop resistance. Check the master cyl for the fluid level, most bikes of your vintage have a 'sight-glass' in the side of the master cyl. There is a 'low' mark, and a 'high' mark. I'd fill the master cyl to the 'high' mark, and replace the cap.
You may want to do a bleed the old-fashioned way: Pump the brake a few times, and hold the brake lever tight. have someone open the bleeder at the caliper and use a 6" length of 1/4" clear plastic tubing into a receptacle, to see the brake fluid come out of the bleeder valve. Tighten the bleeder, and release the brake lever pressure. Now pump the brake lever a few times, does it give you a good feel, and not come back too-far to the handlebar? If the system is full and the bubbles are purged/removed, you should have a ready to rock front brake.
FYI, the screws for the master cyl cap are small tapered M4 machine screws. It's easy to strip-out the head, use a #1 phillips or a small JIS (Japanese Industrial Standard) X-head to loosen/remove these. A well-stocked hardware store may have replacements, or try Mcmaster-Carr for mail-order. I have used hex-head machine screws of the proper thread instead of a tapered-head M4 machine screw, with no problems. No leakage, and still OK today.
I believe that it's in your best interests to take a critical look at your entire system and to replace suspect parts, like what I believe to be your deteriorating-inside the rubber brake lines causing your recurring problem.
At some point, your brake line could develop a delaminated inside, causing a sudden blockage (in-effect, a one-way valve) when you attempt to use the brakes. Think of it as what the medical profession calls an aneurysm. The path for brake fluid to travel is suddenly and totally-blocked, and the brake pressure is not released. If that happens to you, god help you to get-out of traffic behind you safely. You may need to crack the brake line loose at a banjo bolt to release the pressure, allowing you to push the bike off the road.
The entire brake caliper is listed as an obsolete part, not available from the Honda dealer I mentioned Ron Ayres Honda in NC. It's the same problem with the front brake hose. Obsolete/unavailable. You can turn to the web to find a replacement hose from a quality aftermarket company. A local industrial company could duplicate your hose, using either your ends or new ones. They will make sure to use the proper ends, positioned in the proper direction.
Russell makes a stainless braided exterior, and a direct-fit brake hose, $40. I found it online.
A word about the copper washers, they are inexpensive, use new ones. Take one with you to the auto parts store, you can probably find a suitable replacement in a blister pack. I have re-annealed my OEM copper washers, after sanding them lightly to remove any ridges, but if you don't want to do that, just buy new ones and ensure the mating surfaces are clean and flat-no ridges.
An important word, I do not recommend doing the reverse-flush on an ABS-equipped motorcycle. Purging an ABS system is beyond the scope of my directions.
Taking some time to fix things, replacing what's needed and getting back on the road, safely, will be a satisfying experience. Using premium parts like stainless steel jacketed brake lines will improve your braking performance. Take pride in doing a quality overhaul/trouble-shooting of your complete brake system.