Let me throw some apples to oranges comparison with my truck. On the surface it's completely different, but drivetrain wise it's closer to the OP's Suburban. I'm running a 5.3 with a 700r4 (call it an analog 4L60 if you want) but the gearing is identical internally. I am running 4.10 gears, but here's where I differ, I'm running 315/75r16 tires which measure out to 34" and change. Take my barn door aerodynamics out of the equation and only look at the weight and it's pushing over 6,000 pounds for a trip. The 5.3 is otherwise stock internally with true 2.25" dual exhaust with no cats and a H-pipe.
In my case climbing any grades out here like Monarch, LaVeta and Wolf Creek passes is a frustrating experience. I learned pretty quickly that RPM is needed in order to tackle these passes without bogging down and getting stuck doing 30mph in 2nd because I lost all momentum. The sweet spot for mine is 2500 and up. With the 4.10's and tires at 65mph I'm turning 1,800 rpm which is well below my target zone for torque. 75 MPH has me still only turning 2,100. If I'm in 3rd at 65, the engine is right at 2500 rpm and climbs to almost 3,000 at 75. I've learned if I keep it there I don't loose the momentum and can generally keep up with traffic and not be "that guy" holding everybody up. The point I'm getting to is 4.56's would keep the 5.3 wound tighter, but with my tire size negating some of the gain. It only brings my rpm up a couple hundred at any given speed. Shorter tires would get the engine spinning closer to my target speed. However I'm not going to go down in tire size, so it's not an option.
LS engines are great, but in stock form just don't make gobs of torque down low. Gearing with moderate tire sizing brings back in some mechanical advantage to get more out of the engine in stock form. The LS design is one to rev in the first place. Roller lifters, roller rockers are standard equipment when you have to pay through the nose to upgrade an original gen 1 small block. That valvetrain and free flowing heads is what allows the high rpm running happen. Let it spin and keep it wound up.
The solution to my 5.3's need for more power? Remove and replace with an 8.1 and dropping the slushbox for a nv4500 5 speed. I already have the engine waiting. No replacement for displacement right?