Here's what I would do:
I don't have the manual, but I think there should be a way to get 4 individual tracks out at a time by using the monitor and FX sends. For example, it seems you could assign tracks 1 and 2 to bus 1-2 and pan them hard left and right respectively. Then in the MONITOR section, push only the GRP 1-2 button. Then send track 3 out of the FX send 1 jack and track 3 out of the FX send 2 jack. That should give you 4 distinct sends. Actually, I would think you could get 5 by sending track 5 through the tape cue jack, but that won't really help you, because you'll still have to make two bounces.
Anyway, so then you'd transfer tracks 1-4 to tracks 1-4 of the CPU using the above method. Then set it up for tracks 5-8 doing the same thing: tracks 5 and 6 to GRP 1-2 (panned hard left and right, respectively), track 7 to FX send 1, and track 8 to FX send 2. Then transfer those to tracks 5-8 of the CPU.
You'd need a 4-channel interface to do this.
After you get both sets of tracks transferred, you'll just need to align them and use a bit of time stretching to get the beginnings and end to line up. It's surprisingly simpler than it sounds. I've done it several times with a 4-track machine (transferring two tracks at at time and lining them up), and I couldn't notice any artifacts whatsoever.
I hear a lot of people saying that it's nearly impossible to get the tracks to line up, and you don't want to mess with that, etc. But I think that's probably just people parroting what they've heard, and they've probably never tried it themselves. I know from experience that it's a pretty simple task, and it works great.
Do you have an audio interface yet?