It is a steel Jamis Aurora.
Yes, the extractor that I used had the left-hand threads. What I meant was an extractor designed for removing left-threaded bolts. That extractor would be right-hand threaded, so it would drive the bolt out the other side.

If the other extractor doesn't work, I'll go back to drilling.

This was a case of me riding my bike through some terrain more rugged than a road bike is designed for. When I got to the other side, the bolt had snapped and my rack was sitting on my fender. The other mounting hardware I removed to get back on the road looked good, but I'll certainly give my bike a good going over.

A back nut is my last-ditch option.

Thanks.