This seems pretty straight forward.
In terms of storage, I've seen that LiPo's need to be discharged down to a certain voltage per cell for storage. Since this will only be launching 10-20 rockets a quarter (After school program) would it be best to use a charger that has a storage capability?
My primary stakeholder wants the controller to have an internal battery compartment so using larger or heavier batteries instead may not work.
Forget what your Controller wants that does not understand how things work. For LiPo you need to charge outside the device in an area that if fire happens will not cause a problem. It seems that your teachers do not understand the Science
I never charge my RC airplanes or Drones LiPo battery inside them; you don't do that