https://www.scautosports.com/Massimo-Parts/TB410_STARTING_MOTOR_M
$110, not bad.. you might check with Arrowhead to see if they have one that will work.
. but one thing i just thought of, you might ought to check Voltage in 2 places, on the battery side of the starter solenoid, and the Starter side of the solenoid, in rare cases, a solenoid can work, but not pass full voltage/amperage through it . i've ran into it twice on a Murray and JD mower.