Hi,
I wouldn't go with a strap. I would suggest trying out a NeckUp guitar support. I was introduced to them on this forum and tried one out... now I have one for all my guitars. The NeckUp is made of a soft leather that attaches to the guitar with suction cups, or you can attach one end of the strap to the endpin.. this is how I use it on my steel-string. I have a classical as well and I use two suction cups.
It is very comfortable and allows you to have the guitar's neck elevated to a comfortable height (adjustable). You can even elevate the neck all the way up to the standard classical position. The great thing is you achieve the classical position while having both feet planted on the ground (no need for foot rests and having one leg elevated, causing even more back discomfort).
The NeckUp is flexible enough that you can angle the guitar pretty much however you want while still functioning how it is meant to do (something most guitar supports don't allow for). I ALWAYS play leaning back in my designated guitar chair (old student, armless, desk chair with cushioned back support). I lean back and have my guitar elevated and right where I want it!
Check them out, ask around the forum... but beware.. they seam to multiply like rabbits.. I started out with one, now I have three, lol
http://www.neckup.com/Merchant2/merchant.mvc
They sell models specifically for classical guitars with about an inch more height to them, the 6" model. But I had gotten used to my 5" versions, so I just stuck to them.. besides, I don't like my guitar raised that high. I find using the NeckUp to be very comfortable and I wouldn't be without one again (my guitar teacher has one now too after seeing mine, lol)
Here is a quick picture of me leaning back with my classical.. just got home from work, so I'm grubby and my wife rolled her eyes at me when I asked her to snap it, lol. (cruddy cell phone pic)
