Why does my A/C "bump" and cycle super fast at night?
Okay. I've finally figured this out after two fruitless visits from the HVAC service people, a new logic board, and new blower motor capacitor. Warranty jobs, fortunately.

It turns out the culprit was our Nest thermostat. It was hooked up without a C wire. In this configuration, to charge its battery, it periodically closes the Heat circuit for very short lengths of time. Furnaces see that short signal and generally ignore it. With our old furnace, it was no problem with either heat or AC; everything ran fine.

However, with our new furnace (an Aire-Flow, in case you're wondering), when the AC was blowing, having the Nest close the heat circuit freaked out the logic board, which responded by stopping the blower motor while leaving the AC compressor running. I'm not sure why it seemed to happen more at night — maybe something about the times the battery charged?

Anyhow, the solution was to connect the C wire (for whatever reason, the furnace installers didn't) both in the furnace and in the Nest, and everything seems to be working.

It would be nice if the Nest warned you about working without a C-wire, but hey, it is what it is.