The reality of Dark Siding is that each rider can experience totally different outcomes with the identical tire. That said, you make no mention of your weight in your post! Paramount to achieving the "correct sweet spot" in regards to "tire pressure" several factors come into play! Tire Brand, Thread/Tread Design, Side Wall Construction and, of course, Air Pressure.
I speak only of my "non run-flat" experience with a 195/55R16 General G-Max! Comparing the Thread/Tread patterns of your Michelin to the Max indicates a "marked difference" in overall "grove/sipeing" hence a true comparison of performance would be hard for me to articulate.
IMHO I would suggest you lower/drop your tire pressure to 36/38 PSI and start increasing pressure in 1 to 2 pound increments to aid you in finding your "sweet spot"! Even when you find that "magic number" you will experience the "slightest of squirm"! It's simply the nature of "Dark Siding" with a non-run flat car tire! That is the main reason there has been a "shift" to "Run Flats" and their "stiffer" side walls".
As has been mentioned, not every Car Tire is a candidate for "Dark Siding"! The Michelin you have used appears to have a "low rating" in "rain performance" when used on a automobile! That would concern me and may be a culprit to DS performance.
Keep us posted as to your experience with you Michelin! You may ultimately find this tire unacceptable and have to replace it!! Nothing ventured, nothing gained!
Ride Safe
bob109