Chucko,
I have seen this 1,000 times. I would like to give you some advise. Please don't get mad at me, I could be wrong. However, if I answered this way to everyone who had your complaint, I would be right far more times that not. If I were you, I would remove the radiator from my tractor and visually inspect. On these smaller units, I have seen numerous times where a customer does clean his radiator, and the radiator looks to be clean while it is inside the tractor. Upon removing the radiator in my shop, I find that it is not clean, although it did look that was when it was installed in the unit. Also, removed the raidator cap from the radiator (not with hot coolant). Look at the groove or ledge in the top of the radiator that the cap seals on. Is it smooth or is it damaged and erroded? If it is not smooth (it should be raised, don't get me wrong, but it should be nice and smooth), then you need a new radiator because yours is not sealing properly and it will not hold pressure like it should.
As for the thermostat, removing the thermostat will only cause (at least negative effects) the engine to take longer to reach operating temperature. It will not allow the coolant to flow so fast that the radiator does not work. The fins inside the radiator restrict the flow of coolant (due to their size), the thermostat only turns "on/off" the coolants access to the radiator (and regulates how much flow goes to the radiator based on temperature). It does this for the sole reason of getting the engine up to operating temp.
I hope this helped you out some. Like I said, I would get that radiator out and inspect it before I spent any more money or used the equipment again on a hot day. Just my 2 cents.