Scott,

Are you sure all the connections are proper and tight ?

I fear you may have a control problem, if you're sure about the wiring.

To check your new sensor:

with a meter the sensor should read 1,050 to 1,100 ohms at room temperature(78 dgrs)

At 210 dgrs. (boiling water) the resistance should increase to 1,350 to 1,400 ohms.

The erratic cooling fan, and the F3 code(still), leads me to believe its a loose wire connection on the sensor harness.

Once you've re checked and varified the harness and sensor resistance,
you would need a range control board(clock).

You should check those resistance readings at the sensor harness, where it connects to the range control board, for a more complete and accurate reading,diagnosis.
(see attached )

Part number: AP4396964