Ok. You really need to do a compression test. Plugs out and put the plug wires on the grounding posts, throttle wide open(will stop the fuel circuit), compression tester screwed into one cylinder. Crank until the gauge stops moving, should only be a few seconds. Then do the other cylinder. I'd think your oil injection pump would be the 1 in a million to fail, they're that rock solid. Everyone likes to believe they're the demise of their engine on a carbed ski. I say bleed the pump and see if it works. But again, that would be after I did a compression test. If I remember correctly, rfi's have a fuel injector(could be either one) that leaks fuel and washes the cylinder down. When you had the head of did you take pics? It would be nice to see everything. Comp test will tell all, then there's many other things that need to be checked, like fuel pressure, as the fuel pump sock in the tank and the list goes on.........
Oh, what did you need to do to get it to spin by hand?