Sherman- there's a mountain of literature that advises against exposing the kids to new romantic interests too early. The problem is that you aren't going to win that argument with your STBXW. My STBX moved directly in with OW (after swearing up and down he wouldn't) and immediately exposed the girls to her. And she gives them massages. Not a thing I can do about it.
Divorce and Child Custody, much like real estate, is pretty local. You sound like you have a more conservative judge, from what you've previously written. For example you wrote that he took a dim view of cohabitation. This is unheard of in my area. So you never know - you can always run it by your lawyer and see if that makes any difference.