Multi-Tracking TI Snow
 

Folks-
I'd like to record the four voices of my TI Snow to four separate tracks. The challenge is I use an external hardware sequencer.
With the Snow in 'Integrated' mode, I suppose Access expects that you'll use a DAW, so the MIDI path to the TI is obvious and efficient. And you can route out through three virtual audio out's. However, to use an external sequencer, you have to bring MIDI in through the TI's hardware MIDI channel and route it, using the DAW, back to the TI. There's a lot of latency and errors when I do this so either I'm doing something wrong or it's not a workable option. I should note our songs are programmed plus improvised.
I'm planning the following:

Record a live session, capturing only the MIDI data. (I fear this won't include knob turns but I'll live.
Play back the MIDI file one channel at a time so that there's just one instrument out.
Reassemble in the DAW.

Any advice or options?
Thanks,
-CCQ-