If I were to go down the modular route, I'd want to be in a position where I could remain in my existing employment at the end of my training until I'd found a position as a pilot. it may be possible to instruct, if you choose to do an FI rating, around your day job. Many instructors do exactly that.
You'd be able to keep your CPL/ME/IR current using the funds from the day job and sit out the any challenging industry conditions. I don't know how strict the airlines are around theory recency but so long as you can remain current with the actual flying I imagine you'd stand a decent chance when conditions got better.