That makes sense. It sounds like yours is probably cooling via the bypass loop. As near as I can tell, the bypass cooling loop on Deere TLBs is there to prevent sudden overheating if the thermostat fails, and also to prevent surging of coolants having different temperatures. You could just take the thermostat out to see if the problem continues.
That sounds like the correct location for an overflow bottle Tee line. The overflow bottle is not about overheating, it's function is to keep coolant level constant.
There are actually two systems that connect into the air space above the level of the coolant in the radiator. One system maintains coolant level and the other is a relief valve in the radiator cap to prevent steam pressure from causing a steam explosion. Some systems tried to combine both into a single system and that didn't work so well. But if you understand what it was supposed to do it may help figure things out.
What matters to the overflow bottle is the height of the Tee in the radiator hose. JD put that fill hose feed where they did so it would be at whatever level they wanted to maintan as a constant level of coolant in the radiator. They did that because the coolant storage bottle and Tee allows the coolant level to respond to volume changes in the cooling system due to temperature. Coolant is either forced into the coolant storage bottle if the level in the radiator is too high, or it is sucked out of the storage bottle by the vacuum formed if the level in the radiator is too low.
For the overflow system to work properly, the radiator cap has to seal tightly enough to hold a vacuum as well as a pressure. Best to use a new OEM one. Also, the hose from the Tee over to the coolant storage bottle has to be nice and tight without any near invisible internal age splits - if in doubt, just replace that hose. And the hose itself has to be long enough to go to the bottom of the coolant storage bottle. The bottle itself needs to be at the original mounting height relative to the radiator to allow it to work right. Usually the Max line on the bottle is a few inches below the normal coolant level in the radiator. Then the coolant storage bottle should be primed with enough coolant to cover an inch or so above the bottom end of the hose.
The other system in the upper air space within the radiator is a steam relief system that ports out through a hose that goes to the open air....or down to the ground. That system is your safety against a steam explosion. It is usually ported in the neck of the radiator and is activated when steam lifts the bottom seal on the radiator cap against that spring in the cap. When overheating is so severe that it steam is generated, raising the internal seal on the radiator cap allows steam to escape to prevent an explosion. This happens with a sound that will definitely get your attention. That rarely happens, but when it does, the steam has to be allowed to escape freely.
There are a few variations on the system I've just described. Some designers try to combine both functions. You can identify some of those because they also have a pressure cap on the coolant storage bottle.
My hope is that knowing what each system does is helps you with your JD 110. Use it gently, they are nice machines. I wish JD had kept them in the lineup and given them some more development.
rScotty