Well, that seems unsatisfying.
The real question is, was it a customer service issue or a design issue? If it's a design issue, then I don't know what else customer service could do in this case.
In checking the manual, I'd be unhappy if EL34 didn't work, as there are no warnings in there to that effect. One possibility is that the amp has a high plate voltage. It may have been easier to get high voltage EL34 at the time of design, but now perhaps Mesa doesn't carry one in their brand. That seems probably given that Variac mode works fine. You might try Ruby EL34BHT. Make sure you get ones selected for Mesa's bias.
I'd check with Doug's tubes or other reputable vendors. It may simply be a case of which tubes you use. Alternatively, they may have heard of such an issue and have some information. It is still possible that the amp actually has a problem.