Some of the bias towards integrated students tends to come from the airlines themselves. They ring up and specifically ask for these students. There is no easy way round this unfortunately. If an airline asks for 10 candidates for example they generally pick a mixture of modular and integrated students, on the basis of good exam results, or flight training or suitability for the airline concerned. I would think the system is the same at OAT and all the other FTOs. I did a modular course and was put forward with a mixture of other modular and integrated guys.
The only real suggestion i have is to try and work hard, keep your head down and make sure you get on with people. In my experience the people put forward have a good training record, turn up on time, are easy to get on with ( this doesn't mean you have to be a pushover!) and most importantly keep in touch with the FTO. With the best will in the world an FTO can't keep in touch with every ex-student, so make sure you show your face on occasions (not so much you p*** them off), update them with your cv ( they often send the most recent only) and make the people in admin your best friends. They often control the main diary of events and know when airline reps are coming, and with a bit of luck you can have your freshly printed cv on the right desk at the right time.
One last thing, i used to put on my cv that i had completed an approved course of training. This appeared to remove the problem of modular versus integrated sufficiently. I also never brought the issue up in interview as most of the people who read cvs and do the first stage of interviews work in HR and don't really understand the difference anyway.