Oookay... I finally found some time. Let's begin.
I'm not including basic details of how these circuits work; I'm simply sketching out what I saw to be your suggestions and showing you why it won't work.
Your suggestion.
Here we have a successful +12V and -12V, but they must be isolated. In my situation, the grounds must remain the same. Here, if you connect the grounds (which are B and D), you short the battery, and everyone dies. If the grounds did not need to be the same (which unfortunately they do in this project) I could get away with that.
larryn's solution is interesting, and might work, but I've set off on a different path so I'm not going to investigate that one.
I find your attachments explanatory, but not helpful to this discussion as this is elementary to both of us.
My solution in the end is this:
I don't like the fact that I have to use a battery, but it seems there isn't an easy way around it. My priorities here are size and simplicity; it needs to be as small as possible, and with 3 components this isn't too bad.
Thanks to all for the help!