Marine: Boating, Sailing, PWC, GPS and Navigation - Hamilton Jet Pump Siezure. Possible?

I have an early model Hallett 19' Baron. This boat is equipped with a built 351 ford (350 hp) and a Hamilton pump. I suspect that the jet pump may be siezing up. There is a slight leak at the input shaft, only a small drip when the engine is shut down, however sometimes when I'm running 25 to 35 mph the boat just stops cold. When I try to restart the engine it won't turn over. It's just froze up. It doesn't seem to be an electrical problem. The engine just will not turn over. The starter is kicking in but it wont turn the engine over, you can hear it laboring, but no go, however if you wait 5 or 10 minutes it seems to cool down and will start and go again until the next time. Sometimes 2 or 3 times in an outing. Has any one encountered a problem like this? Is this possible?

I have never worked on a jet pump but I would look at the shaft where it goes through a bearing if it's locking up It might be getting hot enough to discolor it.

Thanks for the reply. That's a good point. I'll do that on Saturday when I take it out again.