Yeah a wornout water pump can be insidious with blades corroded down to nubs even if its not leaking. By modifying the T-stat folks are talking about drilling out the collar with small holes. Or there's usually an original T-stat hole that should be pointing up at its highest point. This prevents air chamber from forming at one side or another of the T-stat.

And if it was me, I'd flush it again for good measure using valvoline 6 hr radiator flush. Meanwhile have you thought about a manual toggle switch for the auxiliary electric fan to bypass the automatic fan control?