The first night we tried the encounter it was super chaotic and we were trying to figure out how to make it more manageable. Thinking about it the next day I realized you can't manage the randomness in a satisfactory way so I came up with a call out system instead (similar to calling sides in Wrath of the Machine). It's not perfect but it's very efficient (we actually almost beat it the first time we attempted this strategy but it was working so well people kept falling behind because we were going much faster than all previous attempts). Here's the full strategy:

The "Baller" Method
1. Everyone steps on Plates, room assigns Retainers
2. Retainers call out designated roles they will take (but do NOT call out IF they are a retainer): Spaceman, Baller, or Plate
2. Non-retainers call out the Plates they will take (reserving Plate 2 for one Retainer)
3. Everyone moves to their positions (Spaceman to space behind Beam, Baller to level below Beam, Plate to Plate 2).
4. Spaceman goes into space and calls out Symbol
5. Room dispenses a Ball randomly to one Plate (after first round it’s already out). Ball is caught and thrown to Baller who calls out charging, charges it in white cloud
6. Non-Retainers move to their designated Symbols and clear adds, the two free Retainers move between Symbols and clear adds.
7. Baller throws Ball at the target for the active Symbol
8. Everyone moves back to original positions
9. Room dispenses a new ball; Ball is thrown to Baller who charges it in the white cloud and jumps in beam. Baller throws ball at ship and destroys the ship
10. Everyone moves to gather spot and kills adds; Retainer positions are assigned by room; repeat from 2

Crappy diagram: