Ok first thing sleeping bag,try putting it on inside out. this is what I did when dd discovered how to open hers and once I did it she never got it open again
With regards bedtime make sure you are sticking as close as possible to your old routine, maybe do an extra story or spend an extra few minutes with him lying in bed and have a chat. You could also consider putting a stair gate across the door to stop him coming out. Is the door closed? Can he open it? You just have to keep putting him back with as little conversation and eye contact as possible. Make sure the person who put him to bed is the one who puts him back- tough I know when it goes on for so long but if not it will just become a game.
Also have a look at his daytime routine again. Is he napping? If yes maybe you need to cut it back a bit?
Moving house can be difficult have done it enough times to know and yes it can take a month and more for kids to settle down.
Oh and the 5 am wake up could be down to him being cold as it's apparently the coldest part of the night.