One detail... If the spaces are spaces and the gallows are also
spaces,
In my understanding of the GSH, spaces aren't spaces: they're either nulls,
or a completely separate character, or they have some other function and
are somehow threaded through. Occam's Razor would tend to favour the first
two... but that may mean nothing here. :-)
I therefore don't think it right to start building character-sequence
hypotheses on top of the GSH until more definitive statistical studies of
at least the first two above possibilities have been done.
Gallowspace might also explain the line-end phenomenon Currier remarked
upon: if a GS word finished near the end of a line, the line would then
need to be padded with nonsense to make it "look right".
Also: if the length of the nonsense at the line-end could be (somehow)
determined, that might give a rough lower bound of the length of the first
word on the following line (the next one down, assuming sequential
top-to-bottom writing).
IMO, the unpredictability near (right-hand) line-ends clearly points to (1)
cryptography, and (2) left-to-right encoding. At the very least, the GSH
fits both of these.