Severe keyboard lag after screen replacement

If it was just one of the screens I'd suggest rechecking your work, but there's no way a misconnected digitizer could happen the same way on two separate phones. It seems as though you might be getting some sort of noise on the digitizer input lines that the processor has to sort through and discard while it's waiting for actual touch inputs.

It really does sound like an issue with your replacement screens, but the only way to know for sure is to try a different screen. Do you still have either of the original screens and are they functional enough to verify the touchscreen? Swapping one of the broken ones back in would tell you if it's the new displays or not. If the old screen works fine then I'd have to conclude that something about the new ones is incompatible with your phone. Of course, you don't have to actually replace it; just open it up and take it apart far enough to allow you to unplug the new screen and just plug in the original for testing.

Outside of that, about the only other thing worth trying would be to do a full factory reset of the phone; wipe it back to its original condition and see if somehow that brings the digitizer back in line.