As far as I can tell, the circuit Eric has generously provided outputs a sinewave of 12V amplitude that is shifted 6V upward from the low side of a 0-18V supply. However, this is is not what I am attempting to describe. Please allow me to explain.
Here is an analogy using audio components. A 2V 440Hz sinewave is fed into a 12V amplifier (a 10W kit type) via a 1:1 coupling transformer. So there is no ground reference between the two.
The amplifier is powered from +24V and +12 rails (with no ground), providing the specified potential of +12V. Please refer to attached diagram.
These voltages are provided by two 12V SLA's in series, and a third connected in parallel between their +24V and most negative terminal. The + rail is taken from the +24 terminal of the 2 batteries in series. The "-" rail is taken from the +12V terminal of the battery in parallel.
In relative terms, the resulting signal will look the same as in Eric's spice sim. And, of course, he is correct in pointing this out. But in terms of absolute charge distribution, the two are different. This is what I hope to objectify with my forthcoming experiment.
One further point. Since the negative side of the two batteries in series and the one in parallel are linked, the latter will tend to be charged. This is an unwanted side-effect of this configuration, but I have found no way around it while keeping with the intent. Unless someone can offer better advice, I suppose I will have to rotate the batteries periodically to avoid damage.