Troubleshooting this morning, thinking probably a starter solenoid, but...
1. Oil temperature sensor dropped offline yesterday. Connection seems good to the engine monitor. That's weird.
2. Dropping the cowl - the right exhaust is hanging lower than normal. Hmmm, that's weird. Push it back up.
3. Get settled under the engine and start to work on the starter solenoid. My plan was to actually take the big output wire and just temporarily bolt it onto the "input", or "hot" side of the solenoid. That way, I can just flip the master switch for a second to test how the starter spins the prop. Figured it was just a bit slower and a bunch safer than shorting it while sitting under the engine (mine's not very accessible while standing).
4. Whilst doing that, noticed that something was amiss - see picture below:
Turns out the bolt holding the ground wire to the engine case had wiggled out. It's the same bolt that holds the right exhaust hanger (aha!). The grounding wire wasn't making contact anymore, thus my sudden starting problem (aha!). But the starter did turn a little bit, right? Where was all that amperage going? Well, the oil temperature sensor died when I was trying to turn the engine. I'm thinking at least some of those amps went through the sensor and fried it. No other noticeable consequences to my AF-2500 engine monitor, though - I'll keep an eye.
Bolted the ground wire back on and she fired right up.
Mike Starkey - you're the big winner - it was the ground path after all.
Thanks for all the suggestions, and I think I'll probably get a spare starter solenoid because I'll bet it's only a matter of time, and not much.
Big lesson learned: Use your noodle and don't jump to conclusions. Every indication in the airplane was that the battery and charging system were just fine, so look elsewhere. I almost let the local A&Ps get a little too aggressive on my battery (they really don't know much about AGM batteries like the PC680) and they could've damaged it. They certainly weren't helping troubleshoot the real problem.
Now if only the weather would clear up, I'd be on my way...