I'm sure there's a way in reaper. An engineer freind of mine did a demo session for me with protools. Unfortunately I don't have it commited to memory. But I do have the original session to study.
But it was real 'on the fly' mixing. All channels were recorded to a new pair of stereo tracks. Any changes made during the new track recording showed up just as if we were mixing down to an analog two track. When that was done, all the channels except the 'mixdown' were muted, and the 2 track mixdown was exported to a wav file
If it can be done in pt, it can be done in reaper. You just have to figure out the routing so ALL your existing channels become the source for your new stereo tracks
Sorry, all I can offer is encouragement not know how.
But hey, thats better than being told you can't.
But to play the devil here, why would you really need or want that? In my case I was running a console with real faders. Working in the box, automation would give you the same results.
The only difference being, you couldn't make any on the spot mix changes.