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Most would say not to mix tires and I would have to agree because each tire is made to respond differently so with that said i would just get a new set of rears and wait till they are both worn out and move on to Michelin PS II's its a great tire but $$$$
I have been doing this for 9k+ now and no issues at all. I run Nitto 555 Extremes up front and sticky NT-01s in the rear for spirited driving and Falken's for normal driving and I have had no issues, in fact the 555/Falken's had zero traking issues at the Texas mile where I had them motoring along at 180+
On my CCW 19X11 wheels my 295 BFG KDW's hook and grip corners MUCH better than the 305 PS2's I had. Very noticable difference. My rwhp is 434; with 3:90 gears.
After experience with Michelin tires on sport bikes "not good, they are known to take too long to get up temp. Great for a track but not for the street. I believe the same is true for their street car tires. That's my take.