Well, the good news is that it only affects one lens, a Sigma 10-20mm wide-angle zoom. I can use it on my D5100. The bad news is that the Nikon FX equivalent is going to cost me a lot more. Thanks for your response.
I'll second Tom's point. While you need to be careful, a good used lens can save you real cash. There are many lenses for sale from individual Nikonians through our "I want to sell" and "I want to buy" forums, and there are reputable stores which sell used lenses. I've sold lenses to very happy purchasers who were pleased to get the price break for a lens in excellent condition.
You have, in fact, alluded to a downside of the FX camera, vs. the DX camera. In general new FX lenses cost more than DX lenses, for "equivalent" lenses.