Is it possible to sync two servers separated by NAT?

I've setup an ownCloud server behind a NAT network. Now I want to access it outside the NAT, but I don't have access to the router so I cannot simply setup a port forwarding to solve the problem. So I want to setup another ownCloud server outside the NAT, which will have a public IP. Now I'm wondering whether it is possible to sync files between them.

The reason why I don't simply only use the public ownCloud server is because uploading and downloading files from LAN server is much faster.

You can use federated sharing between them, but the data will stay at the original server. Other option is two sync clients with a file system in between as intermediary ...

But you can only reach the public server from the server behind the NAT. Not the other way round. Did you consider using a VPN? So both servers can talk to each other via VPN. You can even use a VPN service to get you server behind NAT a public IP.