You might consider a normal propped outboard with an aluminum or stainless steel "rock guard". That is a kind of metal 'leg' that extends below the prop and kicks the motor up if a rock is encountered.
My experience with jet drives is that they are susceptible to damage from gravel, sand, small rocks, grass, seaweed, fishing line, small cords, etc. while running in about 2 foot to 3 foot depths. Most manufacturers advise not using them in shallow sandy, gravelled areas since the impellers are rapidly abraided.
you might try rigging a "sculling" oar off the transom for downstream work without using the outboard. Someone described that recently on this site.
While this may sound crazy.... you could try two, used, 16 foot C-Dories. Each would be easy to operate in extremely shallow water. Combined, they'd be a bit less weight than a 22 footer, I think. And you could split the two 25-40hp outboards between the two. One could tow the other. Both could be 'sculled' a bit, especially downstream. You could raft them on calm runs, or two alongside. You'd have private bunks! And, you could probably buy two of them for closer to $30,000 than a 22 footer.
Just a thought, John