The practical issue seems to be the small balance wires, they may not handle the inrush current when first connected?

This is out of the mainstream, but it is possible and some fly guys do connect unused charged packs with discharged packs for storage, but they do it with the main power wires, no balancing. And typically with a resistor for a margin of added safety, limit the inrush.

If you did try the balance wires as mentioned, all of the #1 cells would balance together, and the #2s and so on. The cells in each pack would not be balanced.

Possible option, pick up a parallel charging and balancing harness and use it with your charger to bring several packs at a time to your desired voltage.

Parallel charge cables

Parallel boards

How to: Parallel charging