Unfortunately no details have been released on the "moving" other than they were looking into it (so not even definite) and we don't even have a date for when it might be happening.

Patch 3.3 is supposed to add more wards to the existing housing areas (or at least that was the plan?) so if they're going to release a moving tool it's probably unlikely to be until at least then and that's 2-3 months away, possibly more. I can't tell you what to do with your FC, but that's quite a lot of time to redo all your airships again since you have the parts built already, but it's obviously a lot of work/time to do that, assuming you can actually get a medium house in the very near future.

Keep checking the lodestone, they'll put any updates on that