Were the soundtracks in the DS and PSP versions of FFI & II different from the PSX FF Origins soundtrack? And if so, did they receive their own printings? Or is the PSX version of the soundtrack the absolute latest rendition?

I believe the PSX  "Origins" soundtrack holds the latest "on-disc" rendition. I think a few jingles may have been added in the DS (er... GBA) and PSP games.

Looked at a music dump for the GBA games and there doesn't seem to be any additional music. Still, I can't help remember SEMO hosting a small section with unreleased tracks and the FF1&2 remakes being in there. I'm pretty sure that section of the site no longer exists however.

The FF1 PSP adds a few new arranged boss themes.
The FF2 PSP adds nothing.

Both otherwise use the PSX OST music.

The FF1/FF2 GBA have a new remixed menu theme that is played at the menu where you chose to play either FF1 or FF2.

Mind posting the new boss arranges in the PSP version of FF1, please?

I was actually the one that ran that section on SEMO, but they removed it because it took up too much space and bandwidth. If someone would like to provide a significant amount of webspace for me, I would like to re-upload those music tracks again.

I am out of the states at the moment and the other stuff is on my computer back home. But when I do go back to the states, it is really simple for me to just FTP all the website files right back online and have the site fully functional again if someone would be willing to host the files for me. (And there are a few new things now that I can add). I specialized mostly in tracks from Final Fantasy that did not make it onto OSTs (including trailer and demo music or ones that did not have an OST altogether, like some of the Chocobo games), and a couple other series, like Chrono and Xeno.