Hi Rach,
I think the key might be getting Jack to fall asleep when put down for his night sleep alone. You could try gradually removing parent imput if he is used to having you in/on the bed/cot by standing beside him to fall asleep then gradually move away until he can nod off without you actually in the room. May take some time but would mean not using CC/CIO. Then, if he wakes in the night he should, in time, be able to turn over and go back to sleep without your input (or your input might be to go in give a kiss/soothe, then go out again). 2am would probably be the end of a long sleep cycle for Jack where he stirs and then wants/needs you to help him return to sleep.
I disagree with being told to sleep with your child if it's not what you want to do as it can be detrimental on relationships IMO. If people are happy to co-sleep then that's great for them.