Whoah, no one has still mentioned
http://projectd8.narod.ru/Programs/Java/UniFM.htm which is a J2ME file manager having a module for MOD/S3M/XM playback?
Since late 2011, I had downloaded lots of modules from TMA directly onto my phone via Opera Mini. And found UniFM to play them, yet it indeed requires a lot of resources even with low quality settings, has a long pre-rendering time, stutters on buffer switches, and couldn't play large files at all.
The major benefit is that it is able to play modules directly from archive files, which conserves the disk space a lot, as modules tend to be compressed pretty well. TMA had served them already packed into ZIP files that time.
So sad I did not notice there is a forum on TMA, and thus so many people omitted my suggestion when they desperately needed it...