Replace the 245's with Michelin LTX 265/75/16 "E" MS/2. 3415 max load. You gain 373 lbs load per tire or 746 lbs on the 2 rear tires. Your 2500 HD 9200 GVWR with a 6084 lb rear capacity is due to the 245's max load capacity tires OEM. 3042 X 2 = 6084. Same axle is on the 3500 HD which has 265/75/16 tires OEM and a 9900 GVWR. the 3500 HD is the same exact truck and you know by now how well your 2500 HD truck handles your loaded TC. It will even handle the TC weight even better and safer with the 265's than you have experienced with the 245's. You will be below the load capacity of your rear tires with the 265's.
265's will alter your indicated speed by roughly 3-4% or about 2 mph at 65 mph (will read 63 mph) new 265 tire to new 245 tire as the 265's will travel farther with each revolution because they are a little over an inch larger in outside diameter. The 265's will move your shift point speeds also roughly 2 mph higher. Good to know but means little in reality. When hand calculating mpg's, to be real accurate, multiply your odometer distance traveled times 1.04 for actual distance traveled on the amount of fuel. 265's also increase your traction. Remember that you are going from very worn down 245's to new tread depth larger diameter 265's.