HI,
IMHO air bubbles are hard to keep in the system as they like to rise to the very top of the system that is the top hose, the top of the radiator and one to the coolant bottle.
You said you checked the coolant level so air didn't jump downward from the bottle.

You are right to suspect the temp compensation board as this is what they do.
The car could be running warmer but the board moves in steps and the next step moves the needle abruptly and what may be considered to big of a step in reality.
It is why we, who like to know exactly what is happening, like a gradual rise instead of stages.
Since this car has sat a lot there could be corrosion on the pins of the board if the car sat in a high humidity outside.

The idea of a thermostat sticking closed in the first few cycles after a long shut down is a probability.

I believe this to be one reason to like to use 92C degree Wahler thermostats over the others. They are made of brass and copper of which brass is made of already. Compatible materials conduct evenly.
I have used or should I say ran into Caloric brands, in my new to me, used cars and I had two of them to do the wrong thing. One stuck closed and another failed running too cool.
The stuck closed one turned me around really quick back to the house.
On other domestic vehicles I have had lots of trouble with Stant brand.
I don't even like walking down an aisle and see them bubble packed hanging on hooks in the parts stores.
They are not a device that should be exposed to the public hands!.
I have seen so many of them laying on the shelf below the hooks, where they fell or got tossed, because people lose the place where they got it from knock the next one over off the hook.

The next thing to look into or I should say behind in the A/C condenser and see it the current radiator is missing fins. Thet can rot loose and fall away. If nothing else look for dries grass and bugs.
If this radiator is a high mileage and has lots of years on it it could be dirty on its insides. Plugged up tubes that reduce cross flow to the bottom is not good.
Especially, if you are in a 45 degree air and rain water cooling environment. If you didn't have a thermostat the engine would be running at the bottom of the range or less. The bottom range is 140 degrees. So something is restricting the flow to cool.

You could have the radiator flow tested to see if it needs mechanically cleaned. Most likely if it does not flow enough it may be cheaper to just replace it a three row unit, if it does not already have one.

You can still pull the radiator and clear the lack of fins theory. Then find a garden hose and run full flow through it. All in one side and out the other should be about what the water pump pushes through it. Surely nothing less as a garden hose is only 5/8" to 3/4" in diameter.

What ever you do do not flush a cars cooling system with those flush kit chemicals, with the radiator still on the car. This will only plug up the radiator used or new. The radiator shops will tell you it's the best stuff going to help them sell more radiators.

I hope you haven't already done this?
But then again, it might be an answer?

Phil