Yes, request a specific letter and a general one. Make sure to specify as much in the requests. Then, when you are choosing which letters to assign to which schools, you'll have the ability to assign the specific one to the school it is tailored to.
I second the yoga recommendation. If you can get to a vinyasa class 1-3x/wk, it could really help your back. I felt awesome when I was consistently doing yoga and taking 3 PTs/wk.
I think you were probably wise to not request that meeting, but if they are inviting you, why not? Wear something nice and thank them profusely for their time.