Proper Gears

I have a 00 Silverado 1500 Z71 307,000 miles, had 89,000 on it when I bought it thanksgiving 05. Original motor, Reman Jasper 4L60E put in at 282,000 miles This is my Daily driver. I recently put a 6 inch Rough Country NTD lift. I am currently running 285/75/16 (33") tires. Thinking of going to 315/75/16 (35") around the first of the year when it will be time for a new set.
I am currently running factory 3:72 gears in the front and rear diffs. I have been doing some research and it seems the optimal gears for 35" tires would be between 4:11 and 4:56.
Looking for any suggestions...

According to the math the optimal gear ratio would be 3.92 which would put you right back at your factory 3.72 gear ratio. Not sure something like that is actually available so 4.11 would put you at an effective 3.90 compared to stock tires. It would give you a little more oomph off the line, but have higher RPMs while cruising.

you have in a 2000 4WD 3.73 gears. with the 6 in lift and 33in tires the 4.56 ratio is best . 4.11 will make it better but not the best.

MPG is not a concern with your mods...

2000 was a good year . my 2000 still runs strong 170K miles all original.

Truck had 265/75/16 tires on it from the factory according to build sheet. Any recommendations on a quality gear brand or supplier?

Truck had 265/75/16 tires on it from the factory according to build sheet. Any recommendations on a quality gear brand or supplier? after market gears are china,, problems ...noisey , whine ..special lube due to chine steel .. find scrap yard gears and ask shops that do gear changes on this,,.