Last summer I was in Lithuania, and had to walk a mile home after I had been to the grocery store. I had a large bag that I slung over the opposite shoulder of the load. I usually had a half gallon of milk and a half gallon of juice plus other things in there. I found it was much more comfortable if the strap was near the outside of the shoulder, not at the neck. I had figured out a way to make the strap double at the top, so that one part went over the shoulder and one part went over the top of the arm. About a foot of double strap would be enough.
You could put this foot of extra strap at the top of your sling to keep it off your neck. So much more comfortable.