Tim, sorry to hear about your back & hope you're feeling better again, soon!
When stringing a longbow, I use the push-pull method with no issues.
With my recurve, I use a stringer like you describe (the ones with 2 cups that I have used always seemed less stable to me), and find that the longer string and using both feet on the string works pretty well with very little movement of the block (even with the spandex limb covers on).
That being said, I am always VERY cautious when stringing or unstringing a bow, for fear of injury or damage to the bow.
Again, I hope you're feeling well soon!
-Tony