carringb is absolutely correct. That weight should easily be pulled by the 5.4L, but you will need to downshift and bring the rpm's up. If it is shifting too much, just manually bring it down to the lower gear as needed. I found when pulling in the mountains in the East with my wagon, that when I did occasionally need to go down to 2nd gear, it was better to downshift manually rather than try to get it to do it with the gas pedal because I would need to be to the floor to get it to automatically downshift on its own and then I would let up a little and then it would shift back to 3rd and lose speed. If I manually dropped to 2nd, I could use whatever throttle I wanted and not worry about shifting up and down. A little noisy, but it pulled all the hills fine. My trailer weighs about 5,600 lbs loaded (per a CAT scale) and my wagon pulled it just fine with 250hp and 300 lb ft of torque for over 8k miles. We've circled NY state, been thru PA, been to the Smokey Mountains in TN, etc. from MI. No issues, and that is with less power than your 5.4L. Of course the 6.0L and 6-speed in the Suburban would be better, but you should be fine with what you have, you just need to learn how to use it in a way that makes you happy.
2014 Wildwood 26TBSS - Upgraded with 5200lb axles and larger Goodyear ST tires
2003 Chevrolet 2500 4x4 Suburban 8.1L 4.10's
