Starlifter - You need to check your owner's manual VERY carefully. I have a 2009 Silverado 5.3L, 3.73, 4WD, extended cab, towing package w/ trans cooler. On the surface, it sounds very similar to yours. Per the owners manual, my tow rating is 7500 lbs. Also listed in my owners manual are 98 (count'em!) other permutations of engine, cab, rear end, trans cooling, etc for the 1500 (there are 20 more each for the 2500 and the 3500). The 1500 tow ratings range from 4800lbs to 14,000lbs. So you need to know what you're truck is really good for. Don't believe a thing the salesman may tell you about towing capacity. When a "half ton pickup" can range from 4,800-14,000lbs towing capacity, anyone who blithely says "it can be pulled by a half ton pickup" is full of BS.
Looking on the internet, the 2604 has a GVWR of about 7600 lbs and the 8314 is about 8450lbs. That's definitely over my capacity. My GVWR is about 4600lb, so I feel I have lots of margin. You need to make sure you maintain some margin, too. At least 10%, but 20% is better.
1988 Coleman Sequoia - popup (1987-2007)
2012 Roo19 - hybid (2012-2015)
2016 Mini Lite 2503S - tt (2015 - ???)
2011 Traverse LT, 3.6L, FWD
2009 Silverado Ext Cab, 5.3L, 4x4, 3.73
2016 Silverado 2500HD Dbl Cab, 6.0L 4x4, 4.10