I eventually bit the bullet and bought a better chair (a Steelcase Leap -- see http://thewirecutter.com/reviews/best-office-chair-is-the-st...) for around $850. Man, it hurt to spend that much money on a freaking chair. It felt like ridiculous extravagance. But it wasn't long before my back pains were completely gone.

If you make programming your profession, you're going to be spending most of your life in two pieces of furniture: your bed and your desk chair. There's lots of places where it's OK to cheap out, but don't cheap out on those.