I have found that I am able to play burnt copies of PS1 games on my newer model PS2 by using a PS1 Action Replay. As a discalmer I will note that I had to disable the disc cover sensor for this to work, but that was relatively simple and reversible. I have used DVD Decryptor and Alcohol120% to burn the images without any issues.
I've posted this here both to inform others that this is possible as well as to inquire if this bypass works with other systems. I don't have a PS2 cheat disc, so I am unable to try it, but if anyone else knows or would like to try, then by all means post your finding here.
EDIT: I forgot to mention that this also bypasses region locks. There are some display issues with PAL games on a NTSC console, since PAL has a higher resolution, but even PAL games still render correctly, but with a cropped image.