I think I've just been overthinking how to get my projects to different computers! For some reason I thought you couldn't just move the .tic files from one platform to another, but that doesn't seem to be the case at all. You can just copy the .tic files directly from computer to computer without issue.
Apologies for my misunderstanding! I guess export is just to output a playable product on a given platform? I'm not sure I understand how that works fully, yet.