Something on those lines sounds likely, and the real world precedent is there for some variety and flexibility in how different militaries and other organizations would deal with the issue.
As for the "horizontal warp core" issue, I'd suggest that
a) the blue-glowing cylinder segments aren't solid matter but forcefields, better equipped to deal with the stuff contained within but also far less opposed to the passage of physical objects;
b) the horizontal thing is the same as in the TNG era: a plasma conduit taking the generated power from the actual power generator to the nacelles; the stuff being contained thus is this mysterious "warp plasma", with poorly understood properties that may well allow it (or the energy flowing through it) to go through solid walls of proper design; and
c) this thing is quite durable and damage-resistant, but if something does go wrong with it, mere emergency bulkheads are going to be of zero help. Had Khan continued pounding the Enterprise, we might have seen the ship torn to shreds but this conduit surviving intact, until a final Biblical-level kaboom.
Timo Saloniemi
http://movies.trekcore.com/gallery/albums/twokhd/twokhd0261.jpg
That screencap would seem to indicate that the horizontal shaft does in fact connect to the nacelles.