Well the fact they're still spinning is a good sign. It sounded like one (or both) of your GPU fans had failed.
Looking back over your symptoms, I don't think temps are the (main) problem here. A little warm, absolutely, but an HD7950 shouldn't be reaching shutdown to save hardware level at high 70's.
You've got a 200W GPU, a 125W CPU (maybe more if you've OC'd) and an unknown board.
Options:
1. Your board isn't suitable for OCing and it's temps from other parts of the board that are shutting you down
OR, most likely
2. Your PSU is nowhere close to capably, consistently running those components (I'm surprised it ever did in all honesty).
I assume this setup was built in 2012, maybe 2013? The GPU was from that era, and so was the PSU, from what I can find at least.
Can't find any updated info on those PSUs, but back in 2012 .... those PSUs were being ridiculed over on Johnnyguru - the links no longer work though (shows the age of the PSU).http://www.jonnyguru.com/forums/showthread.php?t=9453
The "new" 650W variant at the time 36A combined on the 12V rail...... so the "650W" PSU was actually a 432W peak.
Yours is the 600W variant, so I assume closer to 400W..... when new.
Add somewhere near 5 years degration on it, coupled with some higher wattage components (125W CPU, 200W GPU + maybe 100W for the balance), that PSU has been running close to it's actual output (when relatively stressed) for a number of years. It's just had it's day IMHO.