A interesting idea. I have thought the extractor problem over quite a bit and researched some other methods. Nearly every gun out there has a spring loaded extractor finger. Most of those have a pivot pin but not all. Marlin had a spring steel flat finger with a circular clip that snapped around the bolt, much like the pocket clip on a pen.
One normal requirement of the extractor, on most guns, is to hold the empty case firmly against the bolt face so it does not fall off until it hits against a ejector at its rearmost travel. The idea is to not drop the case prematurely and cause a jam. In the case of the gatling I don\'t think retaining the case is necessary, only long enough for the case to clear the chamber.
I am surprised that the wire you use, soldered at the end of the bolt has enough flex to \"snap\" over the round during feeding. Also, the wire being so thin, I wonder if wear over time to the edge will be a issue.
How many tests have you performed? Were they with rounds fired in the chamber? (rounds fired in the chamber are tighter and much harder to pull out).
If it works out well, its certainly a easy fix to a big problem.
George