OK, I didn't know about saving as an .sif. That gives the XML formated file for editing.
I exported the vertices of the three BLines using unique ValueBase Node names(Hr1, Hr2 and Hr3), then disconnected the BLines from the exported values.
Next I saved as an .sif file and opened it for editing in gedit.
I found the exported vertice lists near the top of the file and simply removed the lines...
<bline type="bline_point" loop="false" id="Hr2" guid="31CD4192935E1481B07DCD0A2B3000AA">
<bline type="bline_point" loop="false" id="Hr3" guid="D3B13BC02976E62F52DD5F0D60A40D4E">
... that collected the sections all under id="Hr1".
When I reloaded the file its only exported value was a BLine list named Hr1.
When I connected a new BLine to the exported list this is what I got... (tweaked to show out of order connections)
File comment: First joined bline.
JoinBLineTest.png [ 10.77 KiB | Viewed 533 times ]
That shows me it's doable. When I figure out the exact sequence to achieve the expected results I'll post it. Unless someone has got something simpler.