Rats! In the Bilge!
Ugh.
Small hints:

We found rat scat in the cockpit. Not much. A few little turdlets.
We found very little rat scat inside the boat.
Except in the shopping bag where we had the bread. We left it on the floor in the V-berth. Rat got to both loaves.
Here's the other clue: Chewed through the bug screen over the companion way hatch.

We emptied the V-Berth. Carefully. Don't want to get into a scuffle with a scared rat.
Then we went to Lowe's to buy some rat traps. The big-old Victor wire traps and some more exotic claw traps. I killed dozens of chipmunks with the claw traps. I think they're more effective than the wire traps. But maybe that was only for tiny, little chipmunks that didn't reliably trip the wire trap.
So. There's bread in the traps.
Traps are shut up in the V-berth.
We're waiting.
There is, of course, a way out of the V-berth through the bilge. If it's down there, it will have to climb back up to get the bread. We don't like the idea of dead rat in the bilge; it will stink and could be very hard to find.
Sadly, it can survive on chewed hoses and wire insulation. There's likely enough water down there that it can drink from the water that sloshes around on top of the fuel tank.
It may have eaten its fill and then left. That would be ideal, but we doubt it left. There are too many nice places to curl up and sleep in the V-berth. We're not seeing a "trail of turds" anywhere, though.

We're hoping that tonight will draw it out and the sound of a trap will wake us up.
Hoping.
Either way -- dead rat or unknown rat -- we're getting water and fuel and leaving tomorrow. I guess we'll continue to rig traps until we're sure there's no new rat scat.
It's hard to be sure. The water sounds seem to drown out any furtive rodent noises.