we must first postulate that Harry/Hermione get out of this situation and that one of them is able to contact McGonagall while evading control or surveillance.

Perhaps Harry could will a patronus to take an extremely small form?

Persuade enough Muggles to take her seriously

Doable, given enough time. If she is morally flexible enough, she could simply memory charm those at the top of the command chain, but... this isn't the sort of thing I'd imagine her doing.

Anticipate Voldemort's intentions and avenues of attack

This is a problem. Unless Harry explains it to her, I don't think she will understand just how bad the situation is.

Explain these to the Muggles in sufficient detail that the Muggles could devise countermeasures (McGonagall certainly can't devise Muggle countermeasures for them)

I'd seek advice from Muggleborns. But actually, in canon the muggle prime minister at least knows about the existence of wizards. I wonder if the muggles already have a (top secret) plan in place for what to do if wizards attack them?

Do all this in the time frame before Voldemort could take over magical Britain, not to mention whichever Muggles McGonagall has gone to for help

This is the big problem.