If I followed all that correctly your hitch weight is 2,000 lbs or more. The 2013 2500 'Burb has a payload capacity of 2100ish. http://www.edmunds.com/chevrolet/suburban/2013/features-specs.html?style=200427774
You're going to right at the payload limit before you add any passengers or luggage! Max Towing is listed as 9400lbs and you're trailer is very close to that with a GVWR of 9,000.
On paper your trailer and expected load is too much for the 2500 Series Suburban.
With that said if you decide to move forward on it I can make you a lowball offer on your diesel truck! ;)
(FWIW I think the 2500 would do it but I don't think you'd be happy coming from a D/A combo).