If you want a Suburban for towing I would probably try to find a 2500 Suburban. They have significantly higher towing and payload. It seems that many people don't even know they exist because GM never really advertised them. If they would have they may have sold more and thus kept them in production.
I purchased a 2009 2500 Suburban to haul my family and tow my boat; it weighs about 6,500 pounds. A 2500 will have a 6.0L engine which is an extremely durable and reliable engine. The 6 speed automatic in the 2500s automatically downshifts when slowing down and also downshifts to help maintain cruise control speed when going downhill.
Mine was supposedly a former Border Patrol unit. I can tell it used to have a lot of two-way radios and light bars installed. Mechanically it's been fine. It tows my boat with ease.