Oh, and as for the older (classic) with the 8.1 it's not going to be much better.
Here's a copy of the capacities page from the owners manual of an '05.
http://chevroletforum.com/forum/attachments/tahoe-suburban-25/5705d1374424408-need-help-w-towing-capacities-2005-suburban-2500-2005-burb-owners-manual-jpg
Sorry it's so small and blurry, it's a rehost from another website. In 2005 the 2500 'Burb with the 8.1 had a max trailer weight of 10,300 and a payload of 2500ish. Those numbers are still very close, some would say TOO close, to what you're actually wanting to do.
IMHO you shouldn't do this. I don't think you're going to be happy with it if you do.