Dryfits are sealed lead acid gel cells. They are also referred to as "accumulators" The guide # is 197 (ISO 100 - 10 feet). If you have the correct adapter to mount them into an umbrella, the best way is horizontally, parallel to the umbrella shaft.
Buy the power pack. Skip trying to be a rocket scientist. The internal circuit board is complex, plus ---
big plus, the components for running the system are both in the battery pack and in the head, so you need both.