Sean,
You can selectively deliver the differences (changes) that are present in one stream to another by selecting the Configuration Context menu (the one you would use to 'Switch' between configuration contexts). The following steps are based on what I see in 6.0.5 for a project that has CM enabled.
Starting in the new stream for P1 (BL1S1)
On the Right Side of the menu you should see something like the following:
Local Configuration
Create Stream...
Create Baseline...
Compare Configuration...
Deliver Changes...
Accept Changes...
Select 'Deliver Changes...', this will open the 'Select Configuration Context menu'. From here - select the original stream for P1 (S1). The 'Deliver Change Sets' page will open showing the Source Configuration on the left (BL1S1) and the Target Configuration on the Right (S1).
You can either have ALL changes (between BL1S1 and S1) delivered to S1 by selecting radio button 'Automatically Deliver Changes' or select radio button 'Review Changes to Deliver'
Select Next...and complete the steps to merge the desired changes that were made in stream BL1S1 back to stream S1.