Seems fine here, but dead sync is tough to confirm as there is scant lip sync. Little there is looks okay.
All clips are A/V linked, and really can't go out of sync. The issue may lie with your PC's resources in handling multiple 6-channel MTS files.
Here's a workaround that may help...
Download this file, which is a single clip of the entire audio track, and add it to the project. It will be in the Audio File bin (top-left tabs).
Place the red cursor at the very head of the project. Right-click the new audio file in the bin and Place on Sequence as Overlay at Cursor...

Delete audio track 1...
This will UNlink all clips.
Expand the timeline with the slider at the bottom-right to more clearly see each clip...
Use the bottom scrollbar as well.
You have said that the entire track is out of sync. If it's still out, nudge it into sync by dragging audio track 2 left or right, as necessary. Very small movements will make a big difference. The more the timeline is expanded the finer the increments will be as the track is dragged. It should not take much.
If you make a mistake, click <ctrl-Z> to backtrack, step-by-step.
Save Project File AS routinely, giving it a unique # or name, so as not to overwrite prior saves. Using Save Project Files (no AS) will overwrite. From the HOME tab, the AS choice is available by clicking the caret to the right of the Save Project button on the toolbar. That way you're protected, and shouldn't lose anything.