Hello,...
Tape outs. Does the 488 have 8 individual TAPE OUT jacks?
If so, then you're ok on the 488 [output] side.
Go search the TASCAMBBS, the 788 page, and I believe there is info on how to configure the 788 for 8 simultaneous inputs during record, by using the aux return busses, etc, [unless I'm mistaken].
Being not too familiar with the 488 or the 788, I could be mistaken, but I think this is feasible. Is your 488 a mkI (orig) or a mkII? That may make a difference.