We had a 17 premier 5.3 also w/max tow pkg and hauled a jayco 184BH fully loaded (near your weights) and it felt smooth, but like others said good sway bars make all the difference! Distro hitch + sway bars are a non negotiable with me for hauling. Make sure to test how the bars fit cause I recall having issues with ours wanting to rub my bumper to get them clicked up inside before pulling back to lock and install.
We had two pairs of the clip ons (one on our sierra and one on my tahoe) and I will warn you, they were great while on, but those suckers were so hard to get off I thought I'd be ripping the entire mirror off with it. If you always want them installed, go for it, but if you want them to be easily removable don't get ones like this pic.