Why does my engine heat slowly creep up to 235f if the engine is running at cruising speed over higher?

It could be that your radiator is partially plugged.

head gaskets need replacement. Depending what the block and head are made from , all that heat you may have cracked the head . For future knowledge , a car should NEVER reach 225, especially 250 , unless your driving a diesele . The reason your car is pushing coolant into the tank is its boiling . I run a race car on the weekend , and i ran that thing hard , its never sees 190.

If you want to check over the motor first :

Pressurive you rad , you can rent a tool You should see nothing leaking

Check to see if you rad cap is still in good conditon , they go bad

You may a sticking thermostat , no coolant allowed to flow through the block

Easy way to check this , but dangerous , after the engine has gotten to temp , if the bottom rad hose it cold and your top is boiling hot the thermostat is stuck closed

How long ago was the water pump and timing belt changed.

You already know that your fan temp switch is working

What is the condition of your engine oil , is it milky brown in color , thats a dead give away that your antifreeze is mixing with you engine oil