I got it to work, but it's kludgy and I'm sure not the proper way.

The base of the problem seems to be that the ParentKeyValue property wasn't getting properly set in the child object before its Save. So I disabled the autoSaveOnParentSaved setting, and changed my save to this:

        if (lReturn)
        {
            // Kludge! For new links
            if (this.oMemberLink.Entity.numIndID == null || this.oMemberLink.Entity.numIndID == 0)
            {
                String cIdField = (lNewContact ? "newId" : "numIndId");
                int iNewMemberId = Convert.ToInt32(this.oContact.DataSet.Tables[0].Rows[0][cIdField]);
                this.oMemberLink.Entity.numIndID = iNewMemberId;
                
                this.oMemberLink.SaveEntity();
            }
            Response.Redirect("findName.aspx?txtFind=" + this.txtLastName.Text);
        }

And hurray, it works. Now, onto the next big problem (trying to get mmCheckBoxLists to populate properly...