It appears to be boiling down to one of two problem. The exhaust fan has had it (you have a new on enroute) or the pressure switch is bad.
I agree. With both, the old and new pressure switches testing and working the same when on the stove would make me lean hard toward the fan motor. The new fan is rated at 120 CFM at 115 VAC. 3000 RPM. I may put the old impeller on if it will fit just to be sure it moves the same amount of air.