However, the quickest way to a fATPL would be to invest in an Integrated course
Agreed Intergrated courses provide the all important contacts, but quickest? Out of my collgues who have since left the RAF and gone on to complete their civvy licences, integrated was never the fastest. I would say for an unexperienced civilian chap starting afresh this may be true, but with a military flying background the time difference is negligible. At least modular would be based on an individual plan - which may be of benefit - as though integrated is more structured by the course - which of course you'll be used to.
Just my 2 pence worth.