I managed to find a website that hosted a player for MacOS Classic that supports MOD, XM, IT and S3M. I finally found one (mostly by accident, hehe). It's called MacAMP and is a WinAMP clone for the Macintosh. It's also available in a "Lite" version for those who thing 900KB is too large.
To download it (and a lot of other cool/useful software for MacOS Classic), go to:
http://www.mac.org and go to the category "Video/Audio" in the navigation bar to the left. Find MacAMP/MacAMP Lite in the list of software and click it and then download the .sit file with the software. If you don't have any software to unStuffIt .it, you will need to get one. I could help out by hosting a .zip with the same files if someone asks - so be sure to do so if you need it!
I believe the program should work in MacOS 7.x but I am not sure. I have tested it on my Macintosh Performa with MacOS 9.1. I have not heard anything about it being PPC code, either, but you can not be completelly sure without reading the documentation (Which does not comes with it).
Have a good time with good old MacOS Classic!