I was running 2.7 without problems for a week or so before the boot failure yesterday, so the 2.7 Mesa firmware upgrade was at least initially OK. That recent upgrade might be relevant, if it could have resulted in stressing the Mesa hardware in some way, causing it to break after a few hours of use.
I am in Tormach's support queue, so I'll let you all know what they suggest. My expectation is that they will send me a new Mesa card to swap in, in the hopes that that will solve the problem.