The full lock bump/jump seemed to be a big issue last winter, I saw reports of it affecting lots of premium brand cars with low profile tyres a big wheels - its good to see Mercedes has managed to fix it.
I believe it was caused by the tyre skipping/hopping because the rubber is less compliant when cold, which would make sense if the new tyres have softer sidewalls.
With regards to tyres its always a difficult choice, Michelin have fantastic test facilities and are the only tyre manufacturer that I know to produce all the tyre production equipment (they supply this to most other tyre manufacturer's) which allows them to tailor the equipment/tyres to suit.
For instance a lot of cheaper tyres are molded and "stamped" with tread, whereas the Michelin tyres have different compounds spun onto the carcass to allow differing characteristics, such as harder sidewalls for steering direction and a softer centre for grip - etc.
Richard Hammond visited their test centre on an episode of the grand tour to learn about drifting.
I have also found Continental tyres to be very good, and Pirelli although they wear out at a rather ridiculous rate..
