Around 26 PSI for 35s, I run 28 PSI for 33s.
Larger tires require less pressure. The chalk test doesn't work because our oversized tires will never run a perfect tread pattern and because most people don't know how to interpret the chalk. It's funny that you interpreted the chalk as no enough pressure most people go way to low. For offroad purposes we run wide tires on narrower wheels, which means at street pressure you'll never get a full tread contact.
Your jeep must ride like a brick. Larger/offroad tires have stiff sidewalls, our jeeps just don't weigh enough to justify 40 PSI. If you drop your pressure down I'm sure you'll find your ride gets WAY better.
CU Boulder Aerospace Engineering