If one battery had the positive to the cap the whole case would be getting that batteries positive voltage which would include the other cap. So the ground for the 510 would have a problem so to speak.I don't see why you couldn't have one at 0 V, but the other would have to be 3 - 4.2 V and have a balance connection from it.
The bridge between the two batteries would need to be isolated fom the case. And that would be doable easy enough.
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