Water will flow both ways in an aquifer. If it is a good well you might have trouble filling it to within 15 ft of the surface. You would certainly be pushing sand into the fractures from which you are withdrawing water.
The sand is settling in the well because it is too large to be entrained at the velocity in the well. That means that you must substantially increase the lifting velocity with greater flow, or you must get the same flow in a pipe that is much smaller than the bore.
I don't drill or develop wells but I apply engineering to solve problems.
My approach would be to drop a deep well jet into the well and keep it down in the top layer of the sand. I might try jetting a little of the flow (maybe 25% of the expected production of the deep well jet) out the end to stir up the sand in the well.
You will need a pit or large tank at the top to let the sand settle out before you send the water back down for another load of sand. The surface area of the settling tank is the important factor. A small diameter but deep tank is no good. A piece of plastic lining a shallow pit is the best way to settle out the sand.
You don't need a real deep well jet pump but you need something that will produce enough pressure and flow. It is possible that your submersible pump could do that. It will be pumping mostly clear water from which the sand has been settled. Whether or not that pump would work depends on the depth to water and the selection of the deep well jet.
You may wear out the jet but that is a small cost compared to the cost of the operation.
You should assume that the well will be contaminated by the process and you should sanitize the system with chlorine before you use the water.
Someone with a big air compressor might be able to blow it out with an air-lift operation. I'm sure the well guys have equipment and processes for doing the job.