Physical movement between ships in the fleet is complicated. There are small craft designed for it, but they're very old, have gone mostly unmaintained, and were frequent targets for parts salvage back when the systems started failing thirty years back. The teleporters are extremely power expensive, and security keeps a tight watch on them as a result. Trying to move ship-to-ship with a flamesuit, even with a suit booster, is asking to get left behind and lost in the void. Mist teleportation is basically the only possible option for the average citizen - but Mists who can teleport more than thenselves and maybe one other, once a day at most, are very rare, and Mist isn't even one of the more common flame types on the Venus Clam.
As a Mist-capable Sky themself, G could manage one ship-to-ship teleport with one of their siblings, but that would leave the others behind, which would be unacceptable. Getting four people from the Clam to the Lily would be impossible for all but two of the Mists in the fleet, in fact, so basically the only way to go about it is to take one of the cannibalised Sparrows. Luckily for their purposes, G knows a good mechanic.