@ Henrik Yep, agreed on all counts. I tried the LATA solution, too, and then found that PIC12F1501 doesn't have LATA...

Correct ANSELA fixed the problem and allowed me to keep the diagnostics.

I also had time to look at the effects of not setting the ANSELA bit on the analog input. While there was no measurable difference near the power supply rails, at 1.2V input a correct setting reduced power consumption by about 700uA.

I can't explain why, but adding a delay before the SEROUT2 didn't change the duration of the pulse... but removing the SEROUT2 removed the problem... curious.