Kent, at Balfa camp this year, I noticed a couple of people with the "Edirol R-9" portable recording recorders. I don't know anything about them, other than the sweetwater link shown above. And the fact that they want $400 for this thing. At a lower cost, my buddy Randy gets pretty good results with his iriver portable MP3 recorder and a good mic.
Good luck Kent and please let us know where you wind up on this deal.
One more thing about the Alesis Multimix 16 Firewire - it has a two-track in connection, so you play your prerecorded tracks back through a device connected to that input, send that device to the main mix, and use the other channels for the members of your live band. The 2-track input is a standard RCA stereo pair.