This is a tricky subject.
You can run multiple copies of RR at the same time, just start RR with the /2 parameter.
Having said that, you'll have to choose the right combination of video/audio players that allow configuration of WHERE the sound will come out from, and then also adjust RR to control the mixer of the desired sound card. I know you can run the Built-in Video player only with the default sound card (set in windows). I have not looked into the options for VLC, MPC or WMP as far as sound card selection goes, but I know you can have multiple copies of winamp configured for the different sound cards..
This is a MAJOR job, but it "Should" be possible... still before you go out buying stuff, you probably should just test it all with 1 monitor (i.e. by shrinking RR's skin to half the screen) and then testing everything like if it was 2 monitors. As long as you have 2 sound cards, you should be able to test/play with this.