Take the plastic water intake grates off the sides of the leg, you may get lucky and find your rubber chunks in there. If they are NOT there, they're likely under the rear water jacket cover, not worth going after unless you planned to have that cover off anyway. Which you might once you get full water pressure and find that it probably leaks around the spark plug holes. :embarassed:
I'd go ahead and replace the entire water pump: housing, plates, gaskets and all (IIRC there is a kit). Housing is probably all scored up inside anyway, in addition to missing any seals. Use some Vaseline or somesuch to lube the impeller when you re-install, makes it much easier to insert (while twisting!) into the housing without breaking off fins--which does happen.
Use a light hand when installing the pump housing nuts...crank down on those too hard and your impeller WILL get bound up and separate from its center hub.
And never, ever, even for a millisecond, crank the motor without muffs and water or submerged in a barrel...that tiny, undersized little water pump design they put on there will fry a dry impeller before you can blink.
I'd also advise pre-buying a few spare impellers. Despite all precautions, these motors' pumps eat impellers--particularly those of today's "quality"--like candy.
BTW, was there a slinger (like a fat rubber square-profiled o-ring) around the driveshaft just above the pump housing?
EDIT: I feel ya on the mating of the exhaust tube and water tube...terrible design. Just remember: if you can bolt the LU back on without crunching anything, those tubes are in the right place.