If you are comfortable with using command line stuff, I found this little Python script perfect for my needs. I copied my subscriptions from my original instance to two others:

https://github.com/wescode/lemmy_migrate

I don’t know enough programming to know whether the tool could be stealing my authentication, but my passwords are random and I don’t really care if anything happens to those.

Edit: You have to run this when the servers are actually functioning. I was migrating my stuff away from my lemmy.world account because of the overloading there, and the server was pretty slow while it was copying my subscriptions. I ran it again an hour later and it picked up the few subscriptions it missed on the first pass. It’s smart enough to check if the new server has a particular community subscription already in place.