Basically, it's a wheel base/over all length problem.
We have the same tires on a 24-1/2 foot, 2002, E350 Minnie. Unfortunately, our E350 is a 157 inch wheel base. So, we have a long rear end beyond the rear axle. The rear end acts like a wind sail in cross winds. Not good. I think Minnie Winnies are longer than Minnies??? You may have even more wind sail effect.
So far, we have put on new tires and new Bilstein shocks on all four corners. Our Minnie has a little rear end sag. We are having the rear springs replaced next week. I hope that stiffer springs improve the ride in general, not just in cross winds.
I agree with the other posts that you don't want to over inflate your tires.