How many GPM is the pump pulling? If you choke back the pump, how many GPM can the well produce? 11 feet is not a lot of storage and the cone of depression may vary depending on soil condition.
Why did you stop at 22 feet? What are the soil layers up to that depth? Slotted (screen) casing could let in more water initially but if the cone of depression drops, it would not last. It sounds like the well needs to be developed to increase recovery.