I agree that there is a huge array of tools that you can find between letting baby cry in the crib and meeting baby's needs in a way that is detrimental to yourself. It's not always about getting rid of sleep props as much as it is finding the sleep props that work for everyone, because some babies (like my first was) are completely incapable of sleeping without either props or distress. You said you have a wrap, what kind of wrap? Is it the Moby or some other stretchy? Because those are really only comfortable to about 15lbs (or less depending on the mom's shoulders). But you might find a SSC to be comfortable to you, depending on where your pain emanates from, if you were at all interested in finding a carrier that works for you.
You can't always do exactly what a baby wants (rocking side to side on your shoulder), but I'm a big believer in the importance of keeping your baby close to support them through changes you have to make to meet your own needs. If it works for your family for LO to sleep in the cosleeper, can you lie down with baby while she falls asleep and cuddle close to her/stay near so she can feel you/smell you/see you/know you're right there with her? You don't always have to stop the crying (sometimes you just can't), but crying in arms/while being cuddled and reassured can look very different physiologically than being left crying for periods of time (the controlled crying method).