NHL 96 and 97 are definitely busted. Pressing any button during a game just takes you back to the pre-game selection menu
Did you assign a player to a team? By default it will run as a CPU match.
Robin I noticed your spreadsheet lists Clayfighter TE and Clayfighter 2 as working but there were definitely graphical glitches when I last tried them in Canoe
I didn't notice anything out of the ordinary, and I played a good few matches as multiple characters in both. I thought the stage level looked a bit odd with the blank background but apparently that's normal. But really saw no corruption of graphics at all. Have another load up and if you can point them out I'll see if I have the same issue.