Are you nursing him? You may want to try laying down to nurse him to sleep. It may take a while for him to get used to it, but this worked for me.

Good luck!

Yes, I nurse him but if he's not hungry he won't nurse!

It sounds like slinging really meets his sensory needs, so I'd look for similar ways to meet those needs that don't involve carrying him. Swaddling might help since it provides a similar pressure and snugness. He might also respond to being in a swing. You may be able to borrow one from a friend to try it out and see if he'll like it or hate it.

I don't know your back issues, but a different sort of sling might not hurt as much. Some are specially marketed as being great for mamas with back backs.

It doesn't take babies too long to develop new routines. I think as long as you respond to him lovingly and experiment with various things, you two will probably find a routine that works pretty quickly. I know it's hard when you're frustrated and he's overtired though! Good luck!
~Alicia

I don't know the extent of your back problems, so I apologize if this isn't helpful. I was also going to suggest the possibility of a different carrier. What kind do you use? Do you use front or back carries? A back carry might be easier on your back than a front carry. Also do you walk around while wearing him? If so, maybe wearing him and bouncing on an exercise ball would be easier on your back than walking around.

Good luck,
Amy