He didn't barrage and assault because he has more manpower after the siege is over than before....and you can tell from the mana trickle too...
Barrage and assault are two different actions. If he barraged and one of the stacks(*) had some siege pips and otherwise he just sat on the fort, taking it in 4 months seems plausible. Even without barrage, 4 months might be possible with 2-3 siege pips and really lucky RNG (eg. getting a breach for free on the first siege tick).
Alternatively, if you're really cold-blooded, you could barrage, pause, detach all but 1 unit from your army, start your detached units moving away, click assault, and unpause. This way, you lose at most 1k men - your allies bear the brunt of the losses.
EDIT: Alternatively again, you could use mercs for the assault. The losses would come from the merc manpower pool, not your own.
(*) One of the advantages of attaching ally armies to your own is you get to use their generals if they are better.