What recruiter told you that you didn't get a job because you did a modular ATPL instead of an integrated one. That is preposterous!
The standard route still works. I'm 32 now, and started flying when I was 19. Even today, I see people that started at the same time I did, getting their first airliner jobs in their 30s and early 40s. They got their CPL, became instructors, instructed for many years... most are flying jets now and some are even captains.
That "demand" you talk about is just an excuse you use to feel better.