K.Y.
Hey mama, this sounds like my little guy! Four months was a BIG time for my son too. There is a growth spurt around this time, plus he started rolling over (your little guy might be working on this, hence the rolling and wiggling at night). My son also hated the swaddling and we transitioned him to a sleep sack. Finally, my pediatrician suggested that he might be getting too big for his co-sleeper and needed to transition to his full-size crib. Moving him to his crib in his nursery was much harder on me than him. He loved it. This all happened within a 2-week period around his 4-month birthday!
As far as the sleeping through the night, it varies with each child. My son slept through the night for the first time at 7 months. You mention "leaning over the co-sleeper." I kept mine right next to my side of the bed with the side dropped down. This way I could just reach my hand in to comfort him without having to get out of bed. You might want to reposition your co-sleeper for the night.
Good luck and best wishes for sweet dreams for both of you!