I cannot be the first person who has tried this. Any ideas? Can I swap
>the uid and gid between the pi and my user on the pi?
NFS usermapping is a deep dark labyrinth leading you into NIS, NIS+ and LDAP. Do you want to explore this, or do you just want something that works?
You can certainly swap the usernumbers, as long as you also chown the files - I can give you a recipe for that if that's helpful.