This itself, is projection.
If Q isn't military intelligence, then what is he? He/She/They sure as hell isn't a bunch of acne-scarred pre-teens posting while tabbing back and forth between porn.
1. Q may be a group of intelligent, keenly informed people, who began this as a LARP, but soon discovered they'd created a monster too big for them to easily stop or control.
2. Q could also be a Deep State psyop, designed to suck the brains out of the Deplorable right.
3. Q could also be a renegade military intelligence program (as you say), but in the MAGA era, I doubt they'd have to resort to such secrecy and cryptic commmunications. It would be just as easy to leak important data to the public using straightforward, plain language, instead of convoluted word puzzles and cryptic quatrains.
My personal opinion is that the project began at #1 and was then subsumed by TPTB into #2.