We have 8.50 x 6's all around with the airglas nose fork on our 182B.
A 182S is a very different beast than a 182B however.....so none of this probably applies too much, and your airplane probably bests our meager 900 pound useful load by at least a few hundred.. It seems to work well enough on the B. It gives the airplane a very nose high attitude, almost a skywagon like stance. With heavy front seaters and a lot of fuel, care (almost full up pitch trim and full aft elevator in the flare) is needed to avoid a 3 point landing. The tail tie down ring is looking a little flat on the bottom! Never flown an S but have 50 hours in a '78 182RG and from my recollection, that one was pretty nose heavy too.

Related to this, be sure to run a weight and balance with your proposed changes though. On ours, after the battery was moved from the aft baggage to firewall and the bigger nosegear was set up, the empty CG was measured at 33.13".....stock it was about 36.63". When you consider that the forward limit is 33", this is a problem....we always have to ride around with 50 pounds of ballast in aft baggage (state required safety gear takes up a lot of this though).
One of the partners in the 182 wants to put 26 or 29" airhawks on. The plane already tops out at about 130 MPH true airspeed though. Any more drag and we're a cub except burning 2x the fuel and needing 3x the takeoff distance.