This makes good reading - I particularly like the interpretation of the term "batteries" as Starfleet shorthand to mean "fusion reactors". It certainly helps to justify their enormous power output! Whatever their actual construction however, they are a step down from "auxillary power", as evidenced by the two distinct terms in TWOK. Would "auxillary" in this case be the secondary impulse reactors? (the ones that operate independently from the main intermix conduit)
I would however also argue for the existence of some "emergancy batteries" which could provide power to heat, light, air but very little else. In other words, just enough to keep the crew alive in dire situations.
These would be simple rechargeable power cells (like batteries today), but with no moving parts or complicated innards would be virtually indestructible (and non-interfereable), a true option of last resort.
However, in most situations (as you detailed above) I think we are dealing with "fusion batteries".