TBH turning on the heater isn't going to have any impact on how the A/C cycles. All that does is adds heat to the air in addition to cool...you have 2 "radiators" in the heater box that the air flows over...one is the evap (cold) and the other is the heater core (cold if you have the heater valve shut, or warm if you have the heater valve open).
The little thermostat thing (for the A/C dial knob )on the end of the capillary tube is sensing the temperature of one of the A/C pipes as it goes into the evaporator... so it has no idea whether you have the heater valve open or not.
The thermostat switch has a capillary tube as mentioned and is quite fiddly to remove and install as you have to unwrap the butyl wrap on the A/C pipe and position the capillary tube end...not as simple as unplugging a switch and reinstalling. I definitely have a heater box with the knob and capillary tube still attached...could try to remove it and send it to you...but I'd recommend looking at the coolant charge first.
Does the A/C blow really cold? I think a symptom of under-charge would be that it just doesn't get really cold, so the capillary tube isn't seeing a cold enough temp to switch off the compressor. unless you have it turned down to a lower setting..my theory anyway. TBH I think you ought to pop down to an A/C place (Maybe Alex Auto that Voldat use??) and get them to check the pressures/charge.
I'll watch your video and comment further.