Just to set the record straight, there are no brushes in these motors. Brushes are used in DC or AC/DC motors with a commutator. However there is a centrifugal switch in the back end of these motors but that doesn't seem to be the problem since the shaft is seized, or at least tight. That motor looks pretty beat and in that condition, with the corrosion around the cord entry too, I'd wonder what the condition is of the switch and centrifugal assembly which is in the rear under the back cover. I'd go for a new pump. Your time is worth a lot too and you could fuss with this thing and still not have a reliable unit.
Al