wider rims will roll it out a bit, but it more rolls the side walls out. I'm running Velocity P-35 rims and used Conti tires for yrs. Loved them other than the tread face is narrow leaving the sidewalls exposed with the wider tires. I ran a 2.2 Xking last yr on the rear in the snow and it worked just as well as anything I've used before short of a studded.
Conti's expand over time, lightly over inflate them for the 1st month or so when you're not riding ( I used around 40-45lbs) will help stretch them faster. I had 2 sets of Mtn kings, a race king and a Xking and they all came close to the spec after some time, thou never quite all the way and my rim is over 2x wider than yours. Your rim is thin, thinner than the standard from your spec (.9inch = 22.4mm most stock are 24mm -ish )