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jonwvara, I don't think the file is as dangerous as all that, especially if you're working on a bare frame (no components attached). Get a big half round file, set the main triangle of the frame on the back porch with the BB just off the edge over the steps, sit on the main triangle to hold it steady, and file downward with pretty good force. I don't think it'll take very long.
That's pretty much the exact method I imagined when the file was first suggested upthread. Since you can do one side, the flip the bike, then do the other side, you could attack it at a slight angle that would make dinging the threads less likely. It's a tight space to work in, and would require a lot of fast short strokes, but definitely doable.
I like the Dremel-style tool option better, probably just because I have one and use it on a lot of stuff. You can get a full kit with grinding stones, cutoff wheels, etc for about $30 at both HF or Costco, probably a few other places.