According to my book a 1500 Suburban made in 2005 only came with 2 gear ratios available. The 3.42 like you have had a tow rating of 7,400# and the optional 4.10 gear ratio had a 8,400# tow rating. I would imagine you will be able to get the 4.10 gear set from your GM dealer to do a factory upgrade. Just be aware on a modern truck its more difficult than just swapping the gears.
You must have the computer either replaced or reprogrammed and there may need to be some slight changed done to the tranny. Also a larger tranny cooler and power steering cooler may need to be added.
The legal end of this is no matter what you do to your Suburban its max tow rating was set at the factory along with the GVWR and GCWR.
If you are unfamiliar the GVWR is the (gross vehicle wheel rating ) or max load that can be on the truck. This includes the truck itself, passengers, luggage, and hitch tongue weight. IE the weight that is carried on the trucks axles. This max GVWR can be found on the door pillar on the drivers side. You will have a rating for the truck along with a rating for each axle. The axle ratings usually do not equal the GVWR. For example lets say the GVWR is 7700# but you may have a 4,500# rear axle and a 3,800# front axle. The important part is to not exceed the max GVWR while not exceeding either axle at the same time.
GCWR is ( gross combined wheel rating ) and this is in the manual of your truck. It will simply be the max weigh both truck and trailer can weigh if pulled across the scales. Again you must be inside this and not exceed the GVWR or any axle rating while doing so.
Hope this helps. You can change gears, up the HP, put in a bigger engine, turbo, ect but its not going to LEGALLY make it tow more. So at the end of the day no matter what you do you can not upgrade the tow rating of your truck legally.
Chris