Problem is many different issues can share the same symptoms. I honestly doubt your vibration is timing belt related by looking at your video. HOWEVER!! As I type this I just remembered something and this COULD be your issue....your balance shaft module was replaced for a geared assembly.
The balance shaft is ALSO timed up to the engine! To get it set right you need to have the engine locked in place with all the timing marks lined up (like when doing a timing belt change), and then fit the new balance shaft module with a locking tool in place to ensure it is timed correctly to the rest of the engine.
If this was not done and they fitted it by eye, it could be SLIGHTLY out and that will cause a harmonic vibration that will appear in a certain rev range and then dis-appear as it spins quicker.
This could very well be what happened with yours. However...to check it is even more work than checking the timing belt. In addition to all the above I mentioned, you also need to drain the oil, support the engine from above, drop the sub-frame, remove the sump and then check the locking tool (£15 online) fits properly while the rest of the engine is locked in place with the appropriate timing belt locking tools (£20 online).
It is a fair job! However the more I think about it, the more this makes perfect sense, and it is the route I would be going down. From your video it is certainly more of a something out of balance that vibrates at a certain engine RPM and then goes away further up the revs. Slightly out of alignment (1 or 2 teeth) could certainly cause that! Especially as you know yours has been messed with/ changed in the past.
