Update:
Just as I suspected, the prior owner had removed the thermostat. The truck was never warming up to the proper operating temp, which was causing the choke to stay on too long.
Today, I installed a new thermostat (190 degree) and changed the coolant. I took the truck for a drive to get it nice and warmed up, and then I parked it for 40 mins. Afterwards, I went back to crank it up. It start without any further problems.
