You poor thing, sleep deprivation is the worst. Not sure if this is helpful to you or not, as my situation was slightly different, but my bub got addicted to sucking himself to sleep on the dummy. At about 5 months he was waking every 40 minutes between 2 and 6 to have it put back in so we decided to get rid of it. This is quite similar to the feed to sleep association I think, cos they wake up and want the same aid to get back to sleep again. I read The no-cry sleep solution by Elizabeth Pantley and used some of the techniques in there to wean him off it- but essentially just stopped using it to settle him to sleep and used every other method- rocking, singing, patting etc. There was definitely lots of crying so this is not a no cry solution, but I was with him the whole time helping him through it- which IMO is very different to closing the door and letting him cry on his own. We had a couple of very difficult settles but it was not nearly as bad as I expected and within 3 days he had forgotten about it and was self-settling, Since then we have had a few ups and downs with sleeping but he has just got better and better at self-settling. Could you stop feeding to sleep but start rocking, and then gradually go to putting in cot and patting, and then just putting in cot? That's basically what we did- small changes so he gets used to it slowly. I think this is a more gentle way to do it (although there is bound to be some protesting) From my understanding these sleep centres are supposed to respect your wishes so if you want help without CIO then maybe they can still make suggestions?? Not sure though. If you google Elizabeth Pantley and "Pantley pull off" then there is quite a lot of info on the net.
Good luck, I really hope things improve for you.