Yes, I think they need something that matches Cindercone, too. That's largely why I predicted that they are terraporting the tree into the Can of Sky and would use the ship/cage that Sorlie was investigating as the destination cage. It's the only other cage that matches Cindercone that's currently up and running, AFAIK.
Here is the meta-logic: Gee, we find out that Sorlie has a huge terraport cage inside the Can of Sky and that Cindercone is a huge terraport cage, too, and we find that out when a huge tree needs to be moved from where Cindercone is to somewhere else. Surprises can happen, but the Checkov's gun / Duex ex Machina and how it will be used seem rather apparent in this case.
Although I probably don't need to say it, just to be clear, I think each cage needs to be fully enclosed for the terraport to work, so each end needs both halves. (A full ship at both ends.)