I probed the COM with the two input pins floating (A) and with input pins connected to ground (B).
Where is the scope ground connected? And I don't just mean circuit node, I mean physically.
I (and others) pointed this out before, perhaps you missed the significance:
that will be sensitive to physical layout
This will remove an inductive pulse from the scope ground.
Can you take a pix of your layout
When the coil is energized or de-energized there is a pulse of magnetic field that spreads out from the coil, and every wire around it is an antenna. How well those antennas convert the magnetic flux into a voltage depends primarily on the loop area of the circuit. That is all about wiring layout, so how the scope is connected is very important.