Too funny. The OP has a high wall pop-up and it divulged into all this.
OP - I think you mistated your weights. Here is a link to the brochure for your stated trailer.
https://www.jayco.com/tools/archive/2008-select-ct/
As to your original question, it depends on the setup. I had a 07 CCSB Sierra with the 5.3 and a 9000gvwr (6500 dry) 27ft trailer. That combo sucked even with a properly adjusted WDH. Switching to a 07 2500 Duramax was awesome and not so much for the power but the stability was night and day. Power was great too. I now have a HW popup like yours (2010 Niagara) that we tow with our 07 Exp and it's great. A little sag, but no issues.