I picked the right guy, I think. He showed up a couple hours after I called him (at exactly the time he said he would), tore it apart, and then asked how old it was. "About two and a half years."
"Your compressor is almost certainly dead. I could replace it, but it's about $600. It's out of the one-year warranty, but there's a five-year warranty on the compressor, so your best bet is to call Maytag and make them fix it for free. You'll still have to pay a diagnostic fee to the service guy, but Maytag will cover parts and labor." And then he told me the ways that Maytag may try to jerk me around, and what to do about it
"There's a small chance that it's really the (something) relay, but when those go out it's usually because the compressor is about to fail. If they replace the relay and it works you'll pay for the repair, but six months later when it all fails again they'll have to eat the cost."
Maytag sucks. I went three rounds of calling the number in the manual, going through their menus, getting to someone who told me I wasn't in the right place, then gave me the number I'd started with. Finally I found someone who gave me a different number, which turned out to be the right place. And trying to book a repair through their website sucks-- they claim they don't have anyone that services Oakland. Riiighhttt.