So I figured it out. It works now but doesn't make any sense.
I record-enable the track, turn on audio monitoring (NOT on the track, but the control bar), press play, and punch in and out using Record key command and I get no dropouts.
If, however, I don't press Play first but hit Record instead and then I try to punch in and out I get the dropouts.
Why would that make a difference whether I press play, then record or record to start out with?