How can I get this pump casing off the motor?
I figured it out. 

It turns out that part 16 (gasket) and 17 (cast-iron seal plate) (which to me, looked like part of the casing (part 1) came apart to allow the casing to slide off. I didn't realize they were separate from the casing as they were flush with it and painted the same blue color all over. The two pieces popped apart fairly effortlessly at the gasket.