I just realized that the way to make a 16-track mod tune that sounds like "pro music you'd hear on a CD" rather than "computer music file" is to treat the 16 tracks not at all like instrument tracks (like a DAW), but like one big workstation rompler synthesizer with 16-voice polyphony.
I wonder if there's a tracker that's based around this concept (essentially recording MIDI tracks like Cubase and then spreading the notes into mod tracks as needed like a "register allocator").