Second encounter with Greg:
Figured out how he works and did about 1/4 of his health worth of damage. Didn't manage to recreate my "turning invisible" glitch this time, but suspect it might come from landing multiple hits on invulnerable targets while using the swap ability.
Also, death with non-Greg enemies on screen hasn't caused the framerate to die, but both times I died to Greg, the framerate crashed to less than 1fps after a few seconds on the "you died" screen. Not sure why, but restarting or quitting to main menu fixed it instantly.