Java ME isn't necessarily a "bad thing", it has been cut down purposefully. Mobile devices are much more powerful now (think iPhone, ZuneHD, N95 etc.) than when J2ME was conceived. The basic test would be: If you can't run it on JRE 1.3, then it won't run on Java ME.
Anyway, if you are wanting access to KoLmafia from your mobile, I suggest you run an SSH service from your PC at home and use
MidpSSH (or any other Java ME SSH client) to connect to it. You could then run KoLmafia in headless mode (CLI) through your SSH tunnel
It would require you leaving your PC on at home though, of course.
Another option would be to setup a VNC server on your PC at home and use J2ME VNC to view your desktop remotely, although I have never tried this personally as I do not have a data plan on my phone (VNC is going to chew more bandwidth than SSH).