Take a look at the MetalCloke steering stabilizer relation bracket and front diff cover. Moves the steering stabilizer up higher, since it's so low from factory.I'm also on 37's (Nitto Ridge Graps) and frequently drive interstates. With 37's (as you know) air pressure is crucial. Both my 17 JKU and my new JL rolled beautifully on 37's at a cold 29-30 psi.
At 32psi and above I experienced a little bump steer from time to time. I'm replacing my factory stabilizer this winter to alleviate any bump steer at higher pressures. Mostly because I'm going to Moab in early Spring, and want to stretch my gas mileage.
If I were on 35's or smaller... the stock stabilizer would be more than enough dampening. My wife's has had her stock one since 2010. She's running 35's.