Yes, your G's can hold more pressure than a H. In your size tire a F load range tire can only be inflated to a max of 85 psi which is good for 4080 lbs single and 3970 dual. A G tire can be inflated to 100 psi which is good for 4540 lbs single and 4410 dual. A H can hold more than 100 psi and more weight but you will need to look on the side of the tire to see how much higher (probably 120) and how much it can carry at that higher pressure as my chart does not list it.
You use the same table for your H tires as long as the weight/tire is less than the 4540 lbs single for a G.