myproblem, You indicate that you have checked the primary water circuit (engine) and you suggest that the water was not as hot as you would have expected being “a little hotter than you would normally wash your hands in”. If you had good flow from a water faucet this is perfectly normal. If you understand that the water only gets to 200°+ after it cycles several times then you’ll realize why it was not as hot as one might otherwise expect. A single cycle will not bring it to this temperature unless the water flow is very slow and then you can damage your engine. The procedure that you describe did not test the cabin heater core unless I missed something in your explanation. You need to take the heater hoses loose and flush it separately. Be careful not to fix a water faucet hose directly to your heater core because the 30 or 40 pounds of water pressure can blow out the core. It’s not that strong; radiator caps quite often only pressurize to 10 or 15 pounds. Just hold the garden hose to the heater hose with your hands.
As the car runs now, and after it has warmed up, what is the thermostat reading?
One word of caution: Don't just pop in a new part until you positively determine that it's faulty. You would not want a mechanic doing that to you, don't do it to yourself, it gets expensive.