Here is something to consider. There is a thing called an air lift pump. It generally requires the static level of the water to be at least half way up the lift path. It could lift some sand, but not quickly. If it is sand holding the pump down, that could be useful. If it is not, I expect that to not be helpful.
It is powered by an air compressor... I am thinking something around 8 CFM, but maybe less. Read up. Watch Youtube. As I picture it, you would run the water+sand into a trap/sluce, and you would return the sand-free water down the well. That is a much lower CFM than the fast method requires.
This air lift pump idea is why I was asking about the static water level.
So the homemade pump would go down the well, along side of the existing drop pipe. One pipe would deliver air. One would bring up water+sand.
Pretend I reiterated all of my disclaimers again.