toto shuts off like anti-lock brakes, flapper leak?

the toto i have that gets used the most has been having a shut off problem over the last month. After flushing, the tank refills then instead of the refill shutting off cleanly and quietly, it does not. best way to describe it is like the sound of anti-lock brakes on your car and squealing chirping tires on pavement. Initially, the refill would shut off this way and make noise for about 1-2 seconds but then would stop and toilet would be fine. I replaced the flapper this past weekend and it did not really help. Now I can hear the toilet leaking occasionally, and sometimes after a flush it will shut off normally but many times it won't and it's worse. I cleaned the plastic that the flapper sits on where it seals with the scouring side of a kitchen sponge, thinking some hard water stains were preventing an even seal. After I first did it, toilet refilled and shut off great for first two times then went back to leaking past flapper and doing the anti-lock brake shut off.
Do I need to replace the white plastic piece that goes through the tank that the flapper sits on?
What else could cause this problem?
thanks,

Does the water stay below the overflow tube?

Does the water flood over and into the overflow tube?

the water stays below the overflow tube and does not flood over.
tank fills to the normal level every time, problem is when the float mechanism shuts off when the tank is full, it shuts off sporadically like i described. And last night it would not shut off and keep making the noise because there was a definite water dribble past the flapper that i could here.

nevermind, pulled the float shutoff thing (it has the blue gmax cover on it). pretty sure that's the problem, the part where it seals has some blue green crap on it.

www.terrylove.com/korky

just replaced the float/shutoff with the korky 818BP. toilet shuts off like normal now. thanks.

see you in 5 years when it happens again and I forget how i fixed it.