Good product, good instruction, didn't solve the problem.
I read that the random power downs of iMacs were generally attributed to failed power supplies, so I went with conventional wisdom and ordered a new power supply.
Unfortunately the new power supply did not fix the problem. The random shutdowns continued. As the capacitors are fine, the tech at iFixit figures its probably something going wrong on the logic board. I am OK with this because the computer is in it's 10th year of near-continuous use.
I think iFixit might want to add a warning that some iMacs have a diagnostics micro-socket chip located really close to the edge of the power supply sink, so to exercise extra caution in that case.
iFixit offered to accept the return with a small restocking fee (I think that's fair since the unit was not defective). Customer support was great.