Yawn......did that for many miles in a 96 crew cab I had. i was usually loaded to around 9400-10000 lbs towing a 7000 lb travel trailer, with 4 kids, rack, canoe, cross bed tool box. Did not have any white knuckle issues, including coming down the pass from govenrment camp in 30-50 mph winds, with chains on truck and trailer. Timerline to Government camp was worst, 10% grade with the road being really slick!
Make sure you have at least a 10K plate from Wa St, being as you are technically ove 10K, you should get a 12K plate, and you would be legal to 12K gvw.
You do not really need a SW3500, but if you want one........
Marty