Thank you, all, for the advice!
It turned out that the Echo buff was what did the trick. I just kept plugging away tonight without going off to do something else. By the 5th attempt tonight (17th total ;-) ), my hit points had gone from 6200 to over 10,000, and I'm guessing that both my damage output and defenses had increased proportionately. My attacks were crazy-good by that point, and even the Vanguard mechs in the last wave weren't hurting me much.
So, done with it, finally!
It turned out that the Echo buff was what did the trick. I just kept plugging away tonight without going off to do something else. By the 5th attempt tonight (17th total ;-) ), my hit points had gone from 6200 to over 10,000, and I'm guessing that both my damage output and defenses had increased proportionately. My attacks were crazy-good by that point, and even the Vanguard mechs in the last wave weren't hurting me much.
So, done with it, finally!