What you can do is, leave the BAM configured as it is and unconfigure just the other connection for BizTalk.
I would just un- and re-configure Enterprise SSO, Group, BizTalk Runtime and BRE for the new SQL Server.
Because this should work without BAM as well. It is here the same, we configured BAM, but we didn’t used it ath the moment.
What I know about BAM is, that it is not a must have for running BizTalk Server.
Wolfgang