Begbie:

In Reaper, I have been trying to route audio via MIDI by connecting the Space through USB (Reaper sees it as a MIDI device) but I have been unable to do that so far.

Midi does not pass audio; you need a dedicated audio interface.

Most all DAWs these days provide delay compensation (pretty sure Reapers had that for a few versions) to handle the latency accrued when running external processors through the audio interface.