Rolex service is around $800.00.. and they "strongly" recommend all service is done thru them.. No idea what it cost to replace
the back. Last I heard there are three Service centers in the US.. Dallas, Beverly Hills, and NYC.. You may want to contact them for help.
There are other "approved" service centers, but in my experience they all charge about the same... so I went with the one in Dallas.
However, the watch hasn't kept correct time since the last service..