Figure 1. The 'scope CH1 coupling is set to AC.
This switches a capacitor in series with the input. A positive going square edge causes the input to rise with it but discharge at a time set by the 'scope's input capacitance and resistance. A similar effect happens on the falling edge.
Switching to DC coupling should fix it.
Looks like this particular case was an XY problem. I never found how to add my device to PICPgm's supported list, but a slightly different permutation of the Google search terms got me a thread that I hadn't seen yet on Microchip's forum, where someone mentioned a different programmer that I hadn't seen before either.
"Pickle" appears to come ...