By the way, I have been researching the Burb 2500's and Excursions for my family of 7. The limiting factor with the Burbs, either 2000-2006 GMT800 or 2007-2013 GMT900 may be payload, especially if you are loading up with adults. And then the 1000 tongue limit on the GMT900, but you may have payload problems before you get to that anyway. The 2000-2006 Burb 2500's with the 6.0 have the highest payload of all these options, as the motor is lighter than the 8.1. The 2000-2006 are as follows, and the right combo can be extremely difficult to find (I've been looking for months).
Tow Ratings/Payload
6.0 with 3.73 - 7600/2828
6.0 with 4.10 - 9600/2828
8.1 with 3.73 - 10,300/2526
8.1 with 4.10 - 12,000/2526
2007
6.0 with 3.73 - 7500/2273-2561
6.0 with 4.10 - 9500/2273-2561
2008-2009 (Integrated brake controller starts 2009)
6.0 with 3.73 (6L90E Tranny starts) - 9300/2273-2561
2010
6.0 with 3.73 - 9300/2049-2385
2011
6.0 with 3.73 - 9400/2049-2385
2012-2013
6.0 with 3.73 - 9400/2181-2450
All payloads are just what I have found through document search. I wouldn't take them as gospel. Try to find some owners or units on lots to verify with labels or scale tickets. I believe the Excursions payloads come in around 1500-1700. As someone noted above, they are underrated and can be easily upgraded. It all depends on which camp you lie in regarding towing over the manufacturer's capacity.
I am sure you know this already, but you can verify the gearing by the RPO labels in the glovebox (assuming they have not been modified).
Good luck!
Edit: The GMT900 numbers are all 4WD. These tow ratings go up to 9600 on the 2WD's, but I'm not considering these. And also, the 4WD will be in the lower end of the payload ranges because of the transfer case, drive shaft, front axle, etc.