Interesting about the CDA - we're still getting it for Natalie (dairy, egg, cat & dog allergies). We did get our specialist rather than GP to fill out, but don't know if that makes any difference.
Re: the sleeping issues, we had major issues for several months with Nat (i.e. most nights she would only sleep on us in a propped up position), but for us it was directly caused by the nasal congestion she had from her food allergies, rather than her not wanting to go to sleep. Most nights she was just so exhausted and would drop off, but would wake every 10mins because she couldn't breathe
She now sleeps close to 12 hours through at night, and although she still wakes/cries out briefly most nights at least once, she always self-settles and goes back to sleep (we just leave her to it).
I know how awful it is to have sleeping dramas, especially when they had been good sleepers!
I'm now dreading getting the 15 month imms done due to the lactose/egg albumin content in them (but I am pro-vaccination, so will get them done eventually

).
Really hope the elimination diet helps Jake soon