The voltage across LiPo balance pins caught my attention.
Using a 3 series Lipo the voltages are:
0-1: 3.7V
0-2: 7.4V
0-3: 11.1V
Interesting ....
And....
1-0: -3.7V
1-2: +3.7V
And...
2-0: -7.4V
1-3: +7.4V
Those look handy.
Looking towards that target of +-12V ... you could series the balance ports, maybe. Then I realised if you are going to use two batteries you might as well use two lipos for the full +12.6V and -12.6V. Then again series across different trios of cells across the packs might help differentiate out the charge voltage differences between the batteries.