60 series sidewall is more "performance" oriented - as in on road performance. Moving to a 65 series might give you a very limited selection of 10-ply tires but I too cannot understand the logic. It's a half-ton truck not a dump truck. 10-ply tires will ride a lot harder than those P275/60-20R Wranglers so I recommend looking for a genuine LT (light truck tire). There will be a lot more selection out there and you will step up from the P (passenger) tires that came on the truck.
Manufacturers putting P tires on trucks (especially 4X4s) is soooo stupid. I know they do it for the cost but most times you see tires that have virtually no business anywhere other than pavement.
The stock tires on my GMC Sierra Z71 were Uniroyal Laredos. What a joke! I pulled up next to an old man who had more aggressive tires on his Mercury Grand Marquis. When I hit any mud I always needed to engage 4 wheel and use plenty of gas. I didn't dare try to go too far or bite off too much.
What sense does it make to equip a Z71 off road package truck with "car" tires????
My fix was new Cooper Discoverer ATPs. Although not a LT tire they were rated for a little more weight than the Uniroyals and I didn't want anything to do with a stiff wanted ride and rarely haul any real weight.
I think you might want to look at something like the Cooper tires but IDK of much in a 60-series from anyone.