And about this consstent and suspiciously hardware like behavior I'm seeing when trying to install the OS (or even run Windows), where the graphics start off fine but degrade in a few minutes and everything comes to a screeching halt - suggestions on how to proceed from here?
Think I oughta try to find a qualified tech here in Nashville to hand this off to? Lordy this is starting to lok like it could really co$t.
.....I'm looking back through all the mucho appreciated and helpful replies here and remembering now about the booting from the laptop in target disk mode idea from gen_. I think I'll try that next.
To make additional progress in debugging, you need additional "known-good" graphics Hardware to substitute. Your buddies at the Genius Bar at selected Apple Stores may have cards you can try for this purpose. Not all stores sell or have spares for the Mac Pro.
The US$250 Apple-firmware 5770 works in all Mac Pro models. Drivers for accelerated operation first appear in 10.6.5 and later.
The "sticking point" is that Apple only recommends what they have exhaustively tested, and their policy is NOT to test in discontinued Macs. So they only recommend this card with the 2010 model (they don't appear to have tested it with the only-slightly-different 2012 model).
You may be able to buy one from a Vendor with a liberal return policy, try it out, and return it within the 14-day (or other) return window if it does not meet your needs.
You could also contact the vendor of your card for help -- especially as the card appears on the surface to be defective. He may be able to make a quick swap.
Well 2 vendors and 3 graphics cards later I now have one that works - it was the graphics card behind the issues indeed, even though all models I purchased were advertised to work with my model Mac.
The latest vendor who agreed to the swap (thanks for that swapping suggestion Grant, maybe that should've been a no-brainer for me, but I hadn't thought of it) said "3,1 Mac Pros sometimes have issues with specific GT120s".
Thanks to everyone for brainstorming on this thing and getting back in the MacSaddle.