Pull the rear housing off the motor, you should see a
centrifugal switch assembly and some sort of wiring
posts where you connect main power and the windings.
One wire pair will go straight into the field winding.
One pair will have one side going through the switch
to the capacitor to a start winding and back to the
terminal block. This latter is your start circuit. You
may need to disconnect the obvious side of the
start winding, and beep out the other end if two
same-color wires emerge from the winding nest.
But pull both ends of the start winding, swap them
end for end, and check it out - rotation should
start and run reversed from before.
If you're lucky you'll see a legend on the terminal
block indicating start & run, or something. If it's
all soldered or wire-nuts, you'll have to dope it out
electrically. Make yourself a drawing maybe.