Gerber 28-790 leaking from fill valve

I shouldn't have touched anything but the flapper, but I figured I'd upgrade all the "workings" in the tank and be good to go.
Wrong. I've tried 3 different brands of fill valves -Fluid Master, Korky and Brasscraft -and they all leak at the stem. The plumbing person at Lowes convinced me I was wrong and that it was a hairline split in the supply line, so I purchased a new supply line. Nope. That isn't it either.

When I first started looking for help last weekend, I saw a posting somewhere about the Gerber 28-790 tank, and that the Universal Fit doesn't fit.
Any ideas?

By the way, I'm female and I've replaced the inner workings of at least 30 toilets for myself and friends but have never had this issue before.

Thanks!

Make sure you are not using tape on the threads.
All those parts should go on clean.

No tape - it's all clean. I realized my toilet was an early water saving model - looks like there is a bucket around the overflow tube and flush valve. It had cracks all around it. I went back to Lowes, purchased a complete toilet repair AND the special Gerber toilet-to-bowl gasket, put it all together. No more leaks around the fill valve but now it's the flush valve. Took the tank off again, soaked the gasket in warm water so it was more malleable, very precisely put the tank back in place - checked it with my level and left it.
Tomorrow when I have more time and can work from home, I'll try flushing it again and hope I don't end up with another geyser.