Ouch, you've gone through a lot of screens!
I'm not sure if this is your problem or not, but I ran into a similar problem on my granddaughter's iPod Touch where the Touch ID was fine but the button didn't work after a screen replacement. I finally pinned it down to the little rubber nub on the bottom of the button that flexes the metal dome and makes the button click. Somewhere along the line I had apparently managed to knock that little nub off, meaning it took an inordinate amount of pressure on the button before it would click. I didn't find a guide for your iPad, but here's a picture of what you're looking for from an iPad 7.
[image|2831021]
That little black dot in the middle of the button is what you'll want to check. If it's missing you'll need to kludge up a replacement; for mine I found a piece of rubber, cut it to the approximate size and secured it with a dab of glue. The shape isn't critical; the original on mine was square so I just cut a tiny square out at about the same thickness. Don't worry about making it round; it's the height that matters, not the shape.
With any luck that's all that's wrong with your button; after three screen replacements I'd think it's very possible your little nub got knocked off, so this seems like a fair bet; at the very least it's worth checking.
Good luck; let us know what you find!