I just talked to the dealer, gave him the VIN number, and got some info and advice. Here's the info I have:
It's a 5.3L V8. rear end ratio is 3.73. It has the factory tow package. The 'dry weight' of the Suburban is 3360.
I told him I was thinking of towing a trailer weighing as much as 4000-4500# dry, with a hitch weight of 623#. (We are looking at a few trailers, this is the heaviest one). He said it was no problem.
I've gotten a lot of good advice from all of you here, and feel that you have done your homework. Do you agree with him?