Maybe I can make this Michelin chart will post where you can read it. First in reading your post I knew the rears would not need more psi than the front based on your weights so I looked up the chart. I come up with 85 front and 75 rear with enough cushion to not add 5 more psi.
Chart is for axle weights and yours are: 10840 F and 18340 R
275/80R22.5 H
PSI..... 75.... 80....... 85..... 90..... 95...... 100.... 105.... 110.... 115
S... 10140 10620 11100 11680 12190 12700 13220 13580 13940
D... 19480 20280 21040 22040 22700 23360 24020 24820 25640