I pulled a zinger with an armada. My zinger is lighter than the sunset trail you are looking at and the armada was rated for more. It was not a good experience. my zinger weighs 7000 lbs loaded (and was about 5700 lbs dry). My armada was "rated" to tow 9100 lbs. I found out the hard way that a vehicle can rarely tow at max ratings. The stated ratings are for a stripped down model with only a 150 lb driver in it. Add options and passengers and those numbers decrease. In addition to my Tahoe can tow 8200 lbs you need to look at a few more things like payload and receiver ratings. inside the drivers side door you will find a sticker that should say something like "occupants and cargo should weigh less than x lbs". This is your payload and you need to subtract passengers and gear from that weight. The more accurate way to do this is to load up the Tahoe with all gear and passengers that will be in it when towing and go weigh it with a full tank of fuel at the local truck scales. Take the scaled weight and subtract it from the tahoes gcwr to get your adjusted towing capacity. take the scaled weight and subtract it from the tahoes gvwr to get your available payload. this is where your weak point will be. The loaded tongue weight needs to be subtracted from your available payload. the loaded tongue weight should be 13-15% of the loaded TT weight. realistically on average people add 1000-1500 lbs of gear (no matter how light you pack, dishes, clothes, chairs, grills, etc really add up quickly). so you are realistically looking at a loaded TT weight of at least 8000-8300 lbs (quite possibly higher) and a loaded tongue weight of at least 1000-1300 lbs. in addition, what is the hitch receiver on the Tahoe rated for with wdh? to give you an idea my 04 armada had only a little over 800 lbs of available payload with 2 adults, 1 small child and a 70 lb dog in it. My hitch was actually only rated to 910 lbs with wdh. My tongue weight is close to 1000 lbs.
Having been there done that with a truck that was under stated tow capacity but over on payload and hitch receiver ratings, I can tell you my family's safety wasn't worth it. I got pushed all over the road by semis, cars and SUVs passing me. I had a lot of tail wagging the dog situations. The final straw came with mountain driving. The engine struggled going up a 7% grade and the armada was pushed going down a 7% grade. The engine wasn't enough to hold the TT back so brakes had to be used more than desired and resulted in overheated brakes. I hauled horses for 20 yrs and never experienced anything that bad. I threw in the towel after that trip, ended up with an F250 diesel (diesel not necessary but we wanted it) to tow the trailer. Now I have complete contol, one handed driving (no more white knuckles) and feel safe. I have since driven the same 7% grade with the new to me F250. I had to touch the brakes one or two times only as the engine was able to hold the trailer back. Basically, my point is, you need to have enough tow vehicle to control and stop the trailer, not just pull it.
If you are wondering, I was running E rated tires, a prodigy P3 brake controller, and a Reese dual cam (still use the reese dual cam but have integrated brake controller now). The difference really is night and day. I hate to sound so negative but having been there, done that, I would be remiss if I didn't share that story with you. What you do from here, is up to you. If you go ahead with the combo, I would start setting money aside for the possibility of needing a tow vehicle upgrade sooner than later. I would also look into hensley arrow for your hitch. Best of luck to you.
2014 Chevy Silverado 3500 Duramax SRW
2014 Palomino Sabre 34REQS
2011 Crossroads Zinger 26BL --sold