MODs and WAVs are totally different animals (look them up in Wikipedia and learn yourself), so there's little surprise that sticking a WAV to Lemmini wouldn't work.
If the converted file plays at the wrong speed, then clearly you need to try a different converter, or maybe change some settings in the conversion program. Unfortunately I can't really help since I've never tried any WAV->MOD conversions myself. Perhaps if the WinAmp plugin you used to create the WAV version of the Sunsoft music allows you to change the playback speed, maybe you can just make the WAV be a too-fast version of the music, and then maybe after conversion the MOD will be in the right speed.
I suppose 0xdeadbeef can consider adding support for other file formats like WAVs MP3s etc.; that's up to him.