I would have tried to agitate the treated water in the sand point to try to drive the acid solution back and forth through the screen.
In a 3 inch sandpoint, I think you could use a 2 inch pvc with a cap glued on the bottom. Then on the top, maybe have a glued tee with side pipes to make sure the pipe cannot fall into the 3 inch pipe. Push the assembly up and down like a plunger. Your water is 9 ft down, and a 10 ft pvc pipe would be just enough.
How long did you leave the tablet treatment in place? Did you use the whole container?