Danica,
You said that the problem starts as the temp reaches the mid-point on the temp gauge on the dash. Working on the assumption that the sender and gauge are correct, it is not likely that you have an overheating issue.
Before you get too far down the overheating rabbit hole, it might be best to get an infrared thermometer and check the temperatures externally. One with the little laser pointer is really handy to have if you don't have one already. Mine spends as much time in the kitchen as the shop. I should get another one.....
Just start the cooled off tractor and start taking readings at places like the head, the block, the thermostat housing, the upper and lower radiator hoses and the top of the radiator. This will give you a good indication of how the heat is moving through the system as it warms up. Diesels like to be warm so don't be alarmed if you see 195+F at the thermostat housing. As the coolant progresses through the radiator you should be able to see lower and lower temps until it gets back to the water pump.
If you don't see anything much over 200F by the time the tractor starts to sputter, you can be pretty sure it is not an overheat situation. One other place to check is the injection pump housing to see if it is overheating.
I would be leery of removing the thermostat unless you have a reason to do so. If you need to do a clean and flush of the system, by all means pop out the thermostat and check it in a pan of water on the stove with a good thermometer. You will be able to watch it open and close and observe the temps when it happens. I do this with new thermostats before I install them. You would be surprised at how often a new one is out of spec.
In my experience running an engine without a thermostat will most likely cause it to overheat. I have never tried it with a diesel, but I have seen several V8 gas engines overheat when the owner thought it was good idea to remove the thermostat "for better cooling". What actually happened was the coolant was flowing through the radiator so fast it didn't have time to cool down.
One last thought: I am not familiar with which injection pump is on your engine but I wonder if the governor is giving problems. If the governor is not lubricated by engine oil but rather has it's own sump it is possible that it needs attention. The Bosch like clone on my tractor has the governor and injection pump crankcase lubed by the same oil but it is separate from the engine oil. If it is not maintained, the governor can do all kinds of goofy things.
Sorry for throwing another "possibility" at you.