Toilets, Sinks, Showers, Tubs and Disposals - flapper valve problem for old toilet

I have an old standard (before American standard I guess) tank. The flapper that comes closest to working is a fluidmaster with adjustable volume. But the distance from the hooks that go on the wings to the center of the valve is just a little too far (maybe 1/4 inch) and the ball part of the valve scrapes on the far edge of the seat hole, and hangs, maybe 20% of the time. I tried all the other flappers available in home depot/hardware stores, like korky, etc. All have same problem and none have an adjustment to allow for variation in distance between overflow tube (where wings are) and center of flush hole in the tank.
The tank on the inside says "standard", and "K56", and the lid says also
F 4043 03. But the contraptions listed somewhere I saw for this tank aren't really what I was looking for, too complicated. I just need a flapper with the right distance from the wing hooks to the valve center. I tried shaving the rubber off, but couldn't get enough to solve the problem.
Surely there must be flappers that allow for the fact that not all tanks have the same distance from overflow tube to flush hole, but all the ones I have tried are the same, and have no adjustment for that.
This must have been an extremely common tank in the 60's, so I can't have been the only one to encounter this problem.
Thanks for any help! I'm tired of jiggling the handle all the time. John

The American Standard units of that era didn't use a flapper that looks like the units you see today. They used a black plastic hinge valve with a rubber seal. You may need to replace the flush valve assembly to solve your problem. They are still available, go to a good plumbing supply store.

Thanks for the reply. I did call a number of places in Atlanta and did not manage to find anyone who knew anything and could help me. But you may be right, the only solution may be to get one of those old assemblies (which will likely cost more money too). I was just hoping that it would be possible to find a flapper of the right size. The one that is in there now seals perfectly when it does not hang, and would clearly work properly if only 1/4 inch shorter.
Well, I will try calling some more places next week, surely I will eventually find some place that can help. John

If finding parts proves too difficult in your area, you may want to consider the possibility of changing out the toilet.
I've often wondered why they called it "Standard" when all the parts were special.