If you're using Nair, I first strongly recommend NOT trying to do your entire back in one go. Getting the middle parts takes a little time and, by the time you get to the last section, the first section you've applied Nair to will get nicely chemical burned.
Instead, I do mine in four sessions: the entire lower back, then rinse. Second, the deltoids, shoulders, behind the neck, then rinse.
Then the two tough parts -- the middle part of the upper back. I do one half and then rinse before doing the other half and rinsing for the last time.
Yes, it's a pain, but, having given myself a couple of nice chemical burns, I'm wiling to put in the time.
For an applicator for those hard-to-reach areas of the upper back, I use a large wooden spoon. A cheapie is best that's a bit lacquered because it's slippery and doesn't absorb the Nair. Use the convex side to spread it -- much easier than a spatula.
After your last thorough rinse, I also recommend repeating the process with lotion -- it will help with the burning.