"SUCCESS!
It took four tries at three Apple Stores, but I now have a repaired MBP. Having finally mastered the warm-up trick (leave it "on" upside down in an AppleSac [now ColcaSac?] sleeve for 30 minutes, then let it cool), I was able to get the machine to boot (and reboot) to run the NVIDIA GPU test (ASD GPT3TL08-1) twice, passing each time with flying colors. The Genius recommended I leave the machine for an overnight ASD. The store called back five days later to say the machine was repaired.

According to the work order (scanned and posted at http://imgur.com/Jw0yK) the Genius that repaired my machine was able to verify that it would POST and pass the ASD and GPU test, but was then greeted by the "nearly dead machine" problem. Note the comment, "Still suspect NVIDIA GPU failure," and that my logic board was replaced under the NVIDIA quality control program. This was after two prior Geniuses told me my MBP was a CTO machine and therefore not susceptible to the GPU issue, (???)
(BTW: No idea what they mean by that "CTO not susceptible" comment if the MBP is in the affected models/manufactured dates listed in the Apple doc. Why would it matter what other CTO options you selected (GPU was not an option).
- Unless they mean some of the later MBP production CTO orders may have used motherboards that had (later) 8600Ms w/o the issue. Nvidia took a nearly $200M charge over the 8600M failures (est. to cover costs of failures/repl.) in summer 2008 IIRC - so they must have known months (at least) before that was made public and perhaps it's possible -some- later build motherboard stock had 8600Ms w/o the flaw.-Mike)
(he later wrote)
Some notes about my experience:
When I got the warm-up trick to work, I was then able to boot and reboot for about an hour after the MPB cool down. I don't know for certain whether the Genius that actually fixed my MPB was able to get it to boot (I assume from the work order notes that he did), but we were able to run the NVIDIA test twice and the network-booted ASD during the evaluation. Neither test failed. The Genius that ran those tests commented that he'd run the NVIDIA test on many machines, and they always failed in the initial "DOS" (I know it's not DOS) portion of the test suite as shown in the attachment. In my case the test would progress to a MacOS test that included various graphics tests and ended with a check of the GPU's PCIe lane width (anything other than x16 is evidence of failure).

There's also an awkward part to the story. Genius #3 from Store #2 (Genius Bar visit #3) was also working at Store #3 during my successful fourth try. I thought he might try to throw a monkey wrench into that visit considering he diagnosed total logic board failure and recommended the retail replacement, but he didn't.
Thank you for maintaining this (MBP/8600M failures) page for so long. I would not have been successful without its information.
-Drew"

Glad the info/tips helped Drew, but the thanks go to the readers. (And again I wish nobody with one of these affected models had any repair refused.)
  

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