I am forced to remove the thermostat housing when doing a flush job. Since the block drain blocks are no longer accessible, use a leaf blower at that thermostat opening and pray I can blow out most of the water so I can hit my 60-40 mix I need in my neck of the woods.
Ironically, your shop just flushed out the heater core, sounds like a shot in the dark, with scale buildup, entire system should be flushed. Is possible your thermostat is not fully closing that causes your cooling system a longer time to heat up. Only takes just a small crack.