I purchased a Bladefish dive scooter just for this purpose. I will tell you that it sounds great in theory but does not translate well to the "real world." The big problem is anchoring yourself well enough to not just blow yourself back underwater. I even tried carrying extreme weight to help but I was not able to make it work. I even tried carrying a smaller blade anchor and securing myself to the sand but nothing helped. Now, if you are trying to move a lot of sand, I think the jet-ski idea is a great one. I imagine you would have to secure yourself to the bottom with a big anchor/weight and then you could blast away. It probably would not be a monumental task to figure out a bolt-on coupler for said purpose.
I would not recommend a dive scooter for moving a larger volume of sand. I wanted to use mine for quick work rather than fanning for deep hits. For moving sand the size of a typical dig, a scooter would be sufficient, but for moving the large quantities you guys are talking about (10x10) I think figuring out a solution with a jet-ski would be a better move.
As for the prop-wash idea, you need some serious wash to accomplish the results we are talking about. Depending on where you live, you might even need a license as you might be considered a dredging/salvage operation. That and you will be drawing attention to yourself as a treasure hunter, which could cause you tax and legal liabilities/obligations.
I don't want to rain on your parade, as I am always trying to figure out new/different/better ways of finding the goods, but I wanted to join in give my thoughts on this topic. If you can figure out a good way to secure yourself to the bottom then a dive scooter might be your best option.
Good luck!
-Marc