I understand your concerns, touching the underlying video as little as possible makes sense. Especially in the hopes of maintaining as much 'quality' and image information as possible. However the .m2ts format (a form of AVCHD) is highly, highly compressed. It's as small as the computer technology built today can possibly make it without it tossing out a ton of pixels. However iMovie is unable to really edit something so compact and compressed especially if you are trying to edit the video down to the frame level (1/30th of a second). AVCH doesn't have ALL the frames contained in that .m2ts file. It has one real frame out of every 24. All the other 23 frames are 'estimated' or mathematically calculated to determine what has changed from the current frame versus that original 'key' frame. And that means iMovie has to re-generate all those missing frames when it imports your video. So this means iMovie is doing a lot of work just to able to open and playback your video clip in the Preview window.
The format that iMovie uses internally is called the Apple Intermediate Codec (usually contained inside of a .mov file). And it uses that throughout the editing process until you export the final edited version. I think that based on this knowledge you could easily just go to the Share Menu > Export Movie... (choose the large size) and save it to the desktop. This will be in a .m4v video ( a form of .mp4 just with a different 3-letter extension at the end). Take that video and share it out to your Apple TV and see how it looks versus how it appears playing back in iTunes on your Mac. That will be the real test of the kind of quality you can expect.