I was having the same issues. If you are a Mac User, I may have a solution for you: I wrote a script that uses ffmpeg to rewrap the video file from MTS to m4v without touching the video or audio (it just removes the subtitle stream). The trick is that it takes the file's timestamp and embeds it in the m4v meta data.
In a future version I may extract the timestamp from the subtitle stream which actually contains it, but that's not necessary for me.
That means obviously that each MTS file needs to have the right date (which is the case for my cameras).
If you don't trust the app, just open it in the AppleScript Editor and have a look at the source code.
You also need to install ffmpeg from ffmpeg.org to a known path.
You are free to adapt the script to your needs. Please share your results again with us.
Good luck
Here's the file:
https://db.tt/OIrZtF0t