Yes, rule out bad screen, and it sounds like you did that by putting it back on original screen.
iPhone 7 home buttons are finicky, the screws on bracket don't like to be overtightened. What we are seeing now is that the turtle ic (also called U10 in China) on the home button flex itself is easy to damage. This ic controls the transfer of capacitive home button pressure input into ones and zeros that the logic board can understand. If you have an iPhone 7 that has home button not working after screen swap, but touch ID DOES work, then that really points to turtle ic which can be changed by microsolderers.
Torn flex is also a possibility but it sounds like you are being super careful not to do this--especially after you had a failure with the first one! I've seen one with a tiny pin !$$&* of flex damage from tweezers. You can look at the flex under a microscope to see if you are damaging the flex.
Lastly software--in a scenario where you put a home button on a bad screen and then swap it back to the original for troubleshooting you may need to reboot the phone once to rule out the board just ignoring the home button sensor.
good luck!
Jessa of iPad Rehab