A couple of thoughts:
1) The tire load tables are MINIMUMS (or maximum, depending on the way you look at it.) They are NOT recommendations.
2) The vehicle tire placard lists the SPECIFIED inflation pressure - and that is for a fully loaded vehicle. Unless the vehicle manufacturer says otherwise, that pressure is also what they specify for the empty vehicle. Yes, the empty vehicle may not ride as well as it could, but there is a front to rear handling bias that gets changed if you only change the rear pressure.
3) Nowadays, the specified pressure includes some factors so that the pressure is MORE than the minimum specified by the tire manufacturer. That's just good engineering practice (if one were to compare the specified pressure to the tire load tables).
4) If you are towing within the limitations of the vehicle, then the placard pressure is what the vehicle manufacturer specifies. If you are towing outside those limitations, then there is a bigger problem than just the tire pressure.
5) It is common for P type tire to have a maximum inflation pressure larger than the specified pressure for your vehicle - and the max pressure doesn't necessarily add more load carrying capacity. LT tires are done differently.
So be very careful deviating from the vehicle manufacturer's specified pressure - and if you do, be sure to include those factors that the vehicle manufacturer included. They've been doing this a long time and have lots of experience i this area.
And on a personal note, I see no problem using a few more psi than the placard specifies when one is towing - say 3 to 5 - but I wouldn't go up to the max. In this case, 38 to 40 psi.