If you're going to do the thermostat its not too much more effort to remove the water pump, then you can 100% rule it out. Not having any heat through the vents could also be blocked heater taps (common for them to gunk up with age) or the ihk may not be opening them (you can unplug the connector on the taps & they will default to open). If it is the head gasket I wouldn't expect oil/water mixing, but more coolant/combustion chamber leaking, so lots of pressure/air bubbles in the cooling system.
Give me a spade, I'll dig my own hole.
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