Now I'm back to thinking it's a software issue. I tested the Guncon 1 with the playstation port of Crypt Killer patched for Guncon support and it shot perfectly straight, even before calibration. I even patched the playstation version of Policenauts, but the game froze about 15 minutes in, before I got to the first shooting section. I'll probably give it another try.
I guess I should have mentioned, too, that I'm on an unmodified original Playstation and I'm using my light phaser on a Model 1 Genesis both hooked up through composite. For the light phaser guns, I'm running hacked Master system games modified to use port 2 through a Mega SD flash cart. Everything works perfectly, except that all phaser games I've tested have the aiming issue and only certain hacked playstation games have the aiming issue.