Something you need to understand about tire pressures that are posted on the side of the tire and/or the sticker on the vehicle: Those are COLD tire pressures, not OPERATING pressures.
You're correct when you state that the pressure rises as you drive, but that's normal and part of the design. The smart folks who design and build these things know that when a tire is cold and has "X" PSI, it won't rise past "Y" PSI when it reaches its max temp.
So if your tires need to be at 35, that's 35 when cold, not hot. As you drive, they could get past 40 PSI and that's okay. That's how tires react. They are designed for exactly that scenario because tires do not stay cold when you start to drive on them.