Don -
I did contact Arrowhead (sent you a PM). It took a little bit, but they called back and had given me a different Arrowhead part number.
Called Pat's Small Engine (the place I ordered the first one from) and they had the part number Arrowhead provided in stock. He pulled it from the box, measured it out, and all physical dimensions, including pinion gear, matched. They shipped it today, FedEx. If I'm lucky, I'll get it tomorrow.
Thanks a ton for your help, and for pointing me in the right direction. I guess I wouldn't have assumed the 1150 used two different flywheels - I would have guessed the part number with the bigger gear was for turning a different motor.