I know I may get slammed for this but this is what I did out of SHEER desperation (I also had a VERY high maintenance two year old at the time)
I put my daughter on her belly to sleep, I would put her in the co sleeper next to me and prayed that mother's instinct would wake me up if she stopped breathing. She was not swaddled. I would do this for naps as well, if she was in the pack and play or it I was around. If she was alone in her room, I would put her on her back, and she would only sleep for 45 minutes or so. I know the stats on SIDS, and never would have done this but I had no help from DH (working over nights) and I was dangerously sleep deprived so please save your judgement everyone.
Also, because she would usually sleep 8-1030, then wanted to be up until midnight or so, I started giving her a bottle of formula at bedtime, which seemed to hold her over (she was breast fed for all the other feedings). Maybe this would work for the 4 am feeding for your child?