Most airlines recruit anytime outside of the summer period. Recruitment can be as early as October and as late as May. Not always the case though. I've seen charter airlines interview in the Spring, but the start dates were actually after the summer so the opposite of what you'd expect. Scheduled airlines with less of a summer peak will probably just hire you as they need you.
You could argue the sooner you finish means you won't miss out on earlier opportunities. But there are too many variables. My advice would be don't stress, don't rush and a finish around Q4/Q1 would be a nice goal.
P.s Great choice on going modular. Exactly what you should be doing when the industry is as it is. Having no debt too will really take the pressure off if you can't find a job right away.