I want to cut and trim AVCHD .MTS clips without re-compressing, or changing format or file name. How do I do that?

When I'm finished I want the MTS file extension.

Have you tried this?
Aunsoft Final Mate - HDcam assistant software, lossless merge/join without recoding, frame accurate cut/split (http://www.aunsoft.com/final-mate/)

VideoReDo works perfectly for this.

VideoReDo MPEG Video Editing Software (http://www.videoredo.com/en/index.htm)

You would think that Vegas Pro could perform such a "simple" task.