Restore SharePoint Database to new server - What to do about external content type?

I currently run SharePoint 2010 and have a content database back-up which I want to restore to a new server.

I was able to restore to a new server and everything seems to be working, except that I have one list in my previous site which had an external content type in it linking to a database for our ERP system. The ERP system's database will also be located on the new server (same as the new location for the content database). How do I link the external content type from my list to the new location of the ERP database?

One thing which I've tried is to create a new BDC and set up a new external content type within the list. That seems to point to the new location just fine, except that I would have to remap all every single item in the list individually.

Any help would be appreciated.