I am in the same scenario. From what I understand (and I hope its correct) student accomodation is mainly limited to Phase 1 basic training, usually the cadets obtain privately rented accomodation for the later phases and FI once they return from the UK after the ATPL studies.
EFT claim to train quite alot of PPL fasttrack student and modular students, I presume this is the area that takes up the flight instructor phase of the APP program. To hazard a guess their is alot larger proportion of cadets going through EFT as modular students (who do not get offered FI roles) then through the APP integrated program. One of the flying instructors at my local flying club recently got back from the US after training with EFT on a modular basis, he was offered a flight instructor job with them (which is not the norm) because they had a shortage of instructors.
I would be really interested to hear from some previous EFT cadets.