Not sure where you got the idea that it’s not advisable to mount the box via NFS. You can totally do this. I would make some adjustments though.
I would use mergerfs to union multiple mounts into one. You would then download to the local mount which is the drive connected directly to your seed box. Then I would have a remote mount to the nfs mount. You merge these into one so that when you link up jellyfin, it won’t know the difference and you can just stream like normal.
You need to copy files from the local drive to the remote, so you can try and roll your own solution by using rclone or use something like cloudplow which solves this issue as well. Cloudplow uses rclone as well, but monitors for changes automatically.
As far as copying files, why are you using sync anyway? It’s pretty dangerous. Just use move or copy instead. This way you don’t need to keep copies on your computer and the server.
As far as streaming from the nfs mount. You may need to make some changes to the cache settings and ensure they are set correctly.
With a setup like that, you should have no problems though.