Mite be worth making sure the dot on the tyre is sat opposite the valve. Sounds silly but it makes a difference. Just saying.
AFAIK Michelin doesn't have the yellow dot, and besides that, I'm guessing that the dynamic balancing machine should be able to cope and compensate for a wrongly placed tyre.
Those were interesting videos, I've actually seen them in the past but have forgotten about them.
Assuming that a newer rounder front tyre can emphasize weave, as mentioned in the video, perhaps I'll try to run the recommended high pressure on the rear and a lower than recommended pressure on the front to kind of 'square it off' until it wears down a bit.
Or even better (but more of a pain) I could install a new rear, to match my new front, and keep my 4000km used rear tyre for my next change, at which point the front won't be so new anymore.
OK, so today I had some more spare time for testing (I'm in the middle of a long stretch of duty in the military reserve force, due to that mess we had down south, so I'm making the best of my spare time between the guard duties and such

)
At first I reduce the pressure to be 30/30 as per marthy's recommendation, and it did seem to stabilize things quite a bit. The weave was much less noticeable, at times I reached up to 190kmh without any weave and other times it still weaved at around 170kmh (triggered by uneven road surface, current lean angle etc.).
Next I filled up the rear tyre to 42psi, as per the spec, but left the front low at 30psi. This did not make the weaving any worse than before, so I concluded that removing air from the front tyre is what made the difference.
This lead me back to my theory (which was mentioned in the movie), that riding a flatter rear tyre (e.g. used tyre) with a rounder front tyre (e.g. newer tyre) is bad practice, and it may be what caused my weaving with the two different new tyres.
10mm drop on the forks? have you tried it back at the stock height? thats a big change in the rake and it usually results in less stability at high speed.
The weaving started immediately after installing my new tyre, which was before I raised the forks to 10mm in the triple, prior to that my forks were only raised by about 3-4mm.
While experimenting (on my private airstrip), with the lowly inflated front tyre, I noticed that I can eliminate the weave by moving back on the seat. I tested this a few times, and sitting back on the seat (right on the
ridge) at speeds up to 200kmh was steady, while sitting up front right next to the petrol tank would cause powerful weaving at 170kmh. hmm...
This led me to think that it might be related to the reduce trail that I caused, by lowering the triple so much after all. Perhaps when I sit back, I'm causing the front of the bike to raise a bit, and adding more trail... or perhaps simply removing weight from the front wheel has this effect.
So I bit the bullet yet again, and decided to install the rear Michelin PR4 too (praying that this will actually solve the problem), and went out for another fast paced ride.
The bike is back to being perfect 
I can go as fast as I want, over bumpy roads and any angle and the bike is rock steady. Whenever the steering is knocked out of line, by a bump, or me letting go and then hitting one side of the handlebar for testing

, it immediately goes back to the straight line, as it should.
Phew
I've kept my slightly used (4000km) rear PR3 tyre, for future use. Assuming the problem I encountered only exists when installing a
rounder new tyre, together with an older
not so round rear tyre, I sould be able to install the used PR3 tyre in a few months time after my rear PR4 tyre has worn out a bit more (hopefully at least another 10,000km from now). By that time the front tyre won't be so new and round, and it might play together will with the newer PR3 rear tyre.
Conclusions:
1.
Do not install a new tyre, with an existing non-new rear tyre. Installing a new rear-tyre with an older front-tyre may still be fine (or may not). It's definitely safest to replace both tyres at the same time.
2. The Bridgestone T30 may or may not be compatible with the MT-09, my tests are inconclusive. I switched out my new T30 for a new PR4, before identifying the actual problem. Perhaps installing a new rear T30 would have solved my problems too (and saved me about 100GBP). Although this whole post (before I hijacked it) was started by stevecbr, who had issues with his
set of Bridgestone Sport Touring tyres. So possibly the T30 would have weaved too, even if I did install a set.
I might try lowering the forks in the triple, back to the OEM spec, just for comparison to try add more trail and give it a even more stability (playing on the safe side now). I'll reconsider it to see if the slower turn-in really bothers me that much, or perhaps better to trade a bit of turn in time (or force) for a bit of stability. I've also encountered a bit of weaving when accelerating from fast corners, which I always accounted to the soft suspension. Perhaps this too can be reduce by adding a little more trail... it's worth testing as it's a very easy fix to change the forks height back and forth.
So this was a pretty expensive, tiring (, and at times scary) lesson, but I believe that lessons learned the hard way are those that you remember the best. I'm also always willing to pay for education, so the time and money wasn't all for waste.
I'm tempted to add a new post labelled "SOLVED: high speed weave after new front tyre installation", which just points to this thread, in order to help people with a similar problem in the future. Or we can just let them rely on memory, or search through tons and tons of posts, like the rest of us do so many times
Thanks for all your inputs and suggestions, you definitely helped put me on the right track.