Load rating
I suspect you could never get the load rating you are seeking because of suspension difference unless you go w/front diff/suspension conversion at big $$$$+.
Everything aftermarket and up-fitting = additional weight of which is taken away from stock vehicle platform weight capacity. Then when adding or up-fitting strict attention to vehicle center of gravity aka: CG should be main focus, example; install a heavy front bumper then something has to counter it in the back like a heavy bumper and/or other options. Usually front suspension is closer to front wheel center line and rear overhang of vehicle is farther away from rear wheel center line so weight has to be calculated frt/rear to keep within manufactures CG design parameters.
K2500 Burbs have heavy chassis, forged lower control arms, different upper control arms just to name a few and no parts interchangeability with K1500 except sheet metal, glass and interior.
Hub bearings are 3 bolt on K1500 4 bolt on K2500.
Torsen bars are heavier too, install heavy rated K2500/3500 torsen bars and expect to break other parts that are rated 1/2 ton.
K1500 10 bolt rear is not up to the task needs to be replaced w/14 bolt FF.
Then the transmission "4L60e" would not be up to the task and need lots of $$$$+ then a fully built 4L60e can't do it this is why so many switch to the 4L80e and even 6L80e.
Better tire size would be the 255/85/16 it will fit stock wheel and most likely not rub wheel well or fender/bumper.
A diesel powered K2500 Suburban shares many if not all of the K3500 chassis/suspension components excluding dual rear wheel axle.
Considering the cost of trying to get a K1500 to a load rating of a K2500/3500 it would be thrifty to buy a K2500/3500.
IMHO, I Give trying to convert a K1500 to K2500/3500 load levels a thumbs down because of the cost factor!