FC GC switch and housing??

[worldofneil]

our FC leader up and left a while back and we want to change up the company

Not sure if I understand you correctly, but you just need to wait. You don't need to change to a new free company or anything. After the original leader is offline for 35 days it'll change ownership to the next highest member who logged in within the last 7 days.

If we switch which GC our FC is alligned with, will we lose our house?

If your members are mainly in other GCs and it slowly starts switching, that's fine. All houses work in all areas, regardless of the primary GC.