After flushing the toilet, it tends to continue to run. When it is flushed,
the flapper is pulled up which allows the water to escape from the tank,
while at the same time the float falls which opens the valve to fill the
tank with water. All is well to this point.

The problem is the flapper generally doesn't go back down to the bottom in a
timely fashion to plug the escape hole, and the source water begins to fill
the tank again.

The source water apparently causes enough turbulence that it resists the
flapper from falling to the bottom. If I were to manually stop the source
water by lifting the float, the flapper drops to the bottom. I think it
would be fixed if there were some way I could adjust the float to not allow
the source valve to open until the flapper were much closer to closing.
Yet, I've adjusted the float as far as it will go and that doesn't do it.
I also think that if it were a slower flow of incoming water, it might work.

Could it be that someone has used the wrong replacement parts? Someone has
added a 'weight' to the top of the flapper, but that doesn't really help,
and I have an objection to relying on pure Kentucky windage to fix things.

Any help appreciated.