I had Michelin Pilot Super Sport (summer tire) put on all four corners of my 05 slk350. Car handled great (when it was warm outside).
Like everybody else, the rears wore out before the fronts. Because I didn't like how quickly the Michelin rears wore out, I replaced the rears with Continental Extreme Contact DWS (all season tire).
When I did that, the result in the way the car handled was exactly the way you described your car in post #1
. It felt so unstable and unsafe, I put matching Continentals on the front. Getting matching tires on front and back solved my problems. The handling returned to normal.
My case may be different than yours because I mixed summer and all season tires, and I think your Hankooks are summer tires like your Michelins.
I believe the key is to have tires that have equal performance abilities on both ends of your car. To my mind, the only way to insure that is to have same brand and style on all four corners.
I am certainly no tire expert....just my opinion.