I am able to calculate it for you .
Already know now AT pressure of 80 psi ( wich is not the maximum pressure ) but need maximum load of tire and maximum speed of tire.
From you rig already know configuration and that is front 1 axle 2 tires on the road, and rear 1 axle and 4 tires on the road.
Need Gross axle weight Ratings ( GAWR) and also give GVWR ( V for vehicle) and speed you wont go over for even a minute in your use.
Better would be real weighed seperate wheel(pair) loads fully loaded , so inclusif persons.
Advice I give is with some reserve, and officially for filled at 18 degr C/65 degr F. Whenn verry hot outside , as you mention, you should read higher cold pressure ( inside tire temp= outside tire temp). Give the ambiƫnt temp when you read the pressure or fill the tires and I can recalculate the to fill pressure at that moment.