@jxself Hmm, I've bookmarked this to see if any answers appear. I've moved instances once and it worked fine, however I didn't care about the posts I left behind. In future I probably will care.
I know you can export your posts and media by "requesting an archive". The file produced is in ActivityPub format so might be importable. My instance shows no option to import posts and media. I wonder if an admin can do it to restore your account as it was on the old instance.