No thermostat will cause overheating, just FYI
A working thermostat can NEVER cause over heating, thermostat sets MINIMUM operating temp, so has nothing to do with maximum temp
Do you have the heater hoses connected, this is the water pump by-pass and needs to have flow all the time, even if you don't have a heater there needs to be a hose looped from intake to water pump
When its idling after warm up, which Rad hose is warmer, upper or lower?
If its lower then water pump is indeed spinning the wrong way
Lower hose should be 15-20deg cooler than upper hose, if colder then rad is clogged, if warmer then flow is to fast, which causes over heating, because, in effect, there is no radiator cooling
Fan is ineffective above say 35MPH, air flow thru rad from vehicle speed is more than any fan can provide
Fan is there for lower speed, and when stopped, cooling so you fan setup is most likely OK
So my guess is that you have an issue in the engine side of cooling system
Leave rad cap off and start cold engine
There might be a initial surge and some coolant might come out, but just one time
Let it idle and watch the the coolant level, should stay were it is, if its slowly rising and over flowing then you have a blown head gasket or cracked head, period
No mistaking that
You can do The Glove Test, to see which cylinder or cylinders are leaking