I still need to dig more into MD myself - there are many machines I’ve barely even used - that said I’ll offer a few thoughts on achieving ‘warmth’ with MD only
I find the track distortion can be warm in a rather subtle way at very low values, especially with slight modulation to make it ‘breathe’ more. I think the MD track distortion is much more ‘analog’ at subtle settings than the OT lo-fi FX
track EQ and modulating it can also add movement and more warmth to the sound, but it’s usefulness varies
the amplitude modulator can add lots of movement when used subtly, and can greatly add to harmonic richness and thickening, although this often will need to be sculpted carefully with the filter as you venture into more extreme territories
careful filtering of bit-reduced samples can sound rather warm - it’s that old school sampler kind of warmth. in general the filter I think is surprisingly warm if used subtly at low or no resonance
the FX are also very crucial to getting maximum warmth from the machine, particularly focusing on careful filtering on the reverb and delay. Also perhaps modulate the master EQ and/or compressor for subtle or extreme movement of your whole drum bus - although strictly for ‘warmth’ the master EQ and compressor may not always be that useful depending on context
I really need to explore the machines a lot more, but I’ve definitely found some surprisingly organic sounds lurking below the surface here and there - like the granular clap synth produces some raw tones and textures I’d normally expect to have to produce using field recordings - not always the most immediately usable sounds (it is useless to actually use it as a clap as far as I can tell ) but in the right context and processed carefully with MD voice architecture they can really bring a lot of life to a mix in an unanticipated way
edit: there’s also just a lot of gain stages inside MD and places to clip signal, so it’s pretty easy to suck the dynamics out of something, essentially the design does not have seatbelts