Here's an experiment for you.
If you have your stabilized mp4 clips in your Library while having the m2ts clips on the timeline, you can replace each clip without upsetting the timeline "template".
There is a Replace Mode in the drop down menu at the right end of the timeline toolbar. Drag mp4 to the same location as m2ts on timeline and it will replace that clip.
You can then use the Slip feature to get your exact in point by sliding a "ghosted" clip back an forth until you are happy.
You can watch THIS to get an idea of what I am talking about once you have "replaced" your clip on the timeline.