Instead of changing WP_HOME etc, it would be best to enforce a single domain, e.g. local.example.com or shared.example.com and then use the HOSTS file to set that address to 127.0.0.1
This way there is no change to the URLs at all as it is unnecessary, and the shared DB content is consistent (this menu doesn’t work on Alice’ machine because Bob created it on his machine, and he uses a different domain name to Alice )
Also keep in mind your situation has the fatal flaw of sharing post content, but not post attachment files/uploads.