Desperately seeking a processor upgrade. How well will the 976 pair with the 7700?

I would think perfectly.
I too am thinking of doing the same thing.

Just fine. My 976 is paired with an ATI 2005 which is the equivalent of the 7500 (rebadged ATI 2005).

To the O.P. ....Perfectly

976 arrived a few days ago. AMAZING the size difference versus the 990. Just moved into a new place so I haven't been doing much audiophile crap so I was super stoked removing the 990 and getting this baby hooked up to the 7700. Everything's connected, batteries in the new metal-like remove (smooth- move on the remote Outlaws), powered on and got the most disappointing SCREECH through my ML ESL's. Obviously this scared the living crap out of me because my first thought was - - f**& I done blew my speakers out....NO FREAKIN WAY!!!! Even more importantly..why the heck did this happen. First thought...loose connection, wires touching, damaged power cable or interconnect. Ok breath...turns out to be a bad speaker cable. SERIOUSLY. So I had an old set of Blue Jean cables lying around so I slapped those on and NIRVANA. Still very much in the tuning process so I haven't done any detailed listening but I tell'ya, out of the box with manufacture settings, this baby sounds wonderful. Another great job by the Outlaws. Another update in a week or so. :-)