Peg, you say "upstream" which implies river?
This probably won't work, but maybe it's an outside-the-box suggestion that might get some other ideas flowing. There are two areas I see as likely problems which may be insurmountable or irrelevant.
You can buy a submersible pump (intended for powering waterfalls in pods and landscaping) that will move a lot of water. One quick search dropped me on this page
http://pondsolutions.com/high-volume-submersible-pumps.htm
where they have a 1.5 HP pump that costs about $750 and will move close to 300 gals of water per minute. I don't know how that would compare with a jet-ski wash, but think about how long it takes a garden hose to fill up a 5 gal bucket and how much dirt you can move with a garden hose and I think this flow rate could really move some muck.
There are out-of-water versions of these pumps as well.
This pump draws 16 amps. You might even be able to drive that from an inverter from an auto battery (engine running) but you can pick up a small generator that will handle it for under $500. Cheaper than a jet ski.
Having the generator on shore would make sense, as although it could be put in some sort of float/boat (hookah style) you'd want to be really sure there was no way it could capsize and join you in the water. That possible electrical issue is one of the two potential problems I mention. The pump iteslf is insulated (otherwise it would kill the fish!) but if it developed a fault... Second prolem was whether these things are OK with saltwater?
--and putting part of it on shore pops a new idea into my head: how about simply using a gasoline-powered pressure washer? I don't know whether a pressure washer needs positive input water pressure to work (i.e. from the house water pressure) or whether just putting the intake hose into the water would allow it to draw on its own. You'd probably need some serious filtering of the input water, especially if it's sandy. I've seen used pressure washers advertised for under $200, so that would be a real budget option, and if dirty water burns up the pump you're not too badly out of pocket. I suspect saltwater would not be OK here, although if it was used for a few hours and then thorouhgly flushed with fresh it might be OK?
Hey, wicked idea: you could even _RENT_ one
-- Big boat folks - how much "wash" do you get from a scooter? If the obviousl electrical issues prove to not be a problem might the a pond pump with a long hose be a better way to wash out under rocks and so forth? That's probably been done a dozen different ways before, but perhaps this is a cheaper version? That same page has pumps that will push 1400 gals a minute which is probably way more than a diver could control...
Bob.