I normally play snes games using zsnesw151. I don't have any problem as you stated.
Also, I patched it using Lunar IPS.
I suspect your Megaman X3 rom is not clean. You might have modified it.
Try to download a new rom.
Both headered or unheadered will work.
Ok, it looks like Lunar IPS worked. Maybe my other tools screw up the 4.0 patch. It's strange that snesRomUtility didn't like this patch but Lunar IPS did. Anyway, I would like to report a bug about Zero boss room. After X warned Zero, I switch back to X and the door won't open until I had to go back and off screen the door and go in again. That's when the door open for X.