All of the above plus my thoughts:
The Alpha has a bit more front end weight with the CI diff and V8. I have to look that up but total was not much, I think, maybe not that much. The OEM shocks by Tennco on that offroad package I believe are a bit different than the ones with the I-5 adventure. I use the Bilstien for now. They seem to fill the gap and are one of the few shocks with the clevis mount on the bottom, that fit. Stiffer is not always better but control in each direction is what I want. I think in my case they tamed down the bouncing as I run lots of gravel and dirt Forest Service roads that have stutterbumps. I started feeling the OEM shocks failing around 27,000 miles and lots of wheel hop. I keep shying away from shocks designed for extended higher speed constant running with the external reservoir to dissipate heat like in desert conditions since I rarely do that and expense. I'm not ruling them out, I just have not found the length I want either. There seemed to be some confusion on the specs on some of those and mounting issues, for now. The Alpha torsions are stiffer as well, but I'm not sure that is an advantage or not on steep hill climbing and the bouncing issues. More controlled movement might be the desired set up for that. I guess it's all dependent on conditions and driver technique.
I could tell a difference in the Alpha after having an 06 first and then running the same hill climbs.
Cranking up the torsions or a lift will also, in my opinion, lighten the front end attitude and will require different driving technique.
Slap a brushguard/winch mount and winch up there, like a Warn Power plant and that moves some weight forward.
Like you mentioned, I also keep my extra weight behind the front seats down low with the rear seat removed except now I keep the single seat with my granddaughters "throne" in there most of the time except on trips. I also rarely carry an extra spare but when I do it is on a light weight rack just behind the sunroof or mid vehicle not at the back end on a full length heavy rack.
On really steep hill climbs the 06 would start to do that as I reached the steepest part, had lost some moderate speed and the weight to tire patch area became inadequate to propel the H3. However, (one of my favorite words) engaging the rear locker BEFORE attempting these same obstacles reduced that front end bouncing by pushing the front end forward rather than as much hopping while losing traction in one area. The source by the way on IFS of broken tie rods, cv shafts and such. It's the sudden stop that kills them.
That type of wheeling here is why I sometimes think the front locker on the lighter end might not be a cure all. I can see going up against a red rock wall that having the front end locked will pull the front up and then the rear locked push it on up, when possible.
It also helps at some point to just shut er down, back down and get a different line rather than mashing the skinny pedal and keep hoping, or is that hopping? I think the lower gear ratio gives more controlled power to the ground and reduces the tendency to use excess speed. The H3 also has a reduced sensitivity of the throttle in low lock helping to prevent over compensating by spinning up the engine and tires.
If you are comparing your H3 to other lighter vehicles on the same obstacle your going to have to come up with the conclusion it may take a different approach for the H3. In some cases an H3 will hit it right while the next may not. I have learned in a large group to give it a try and if it's not your day, take a strap and live to die another day for the benifit of the group and your vehicle.
I still sense a bit of competition in your blood about that which is good just don't let it affect the way you drive.
I always say with my friends, in Heeps and Rovers, hey lets just see what the H3 will do, I don't know either. Our first few runs at Superlift with the group that guides in 06 was our first chance to see what the H3 would do. I was happy with the performance and the vultures sort of walked away quietly after having come back to the edge to see what the H3 would do. I was impressed at how it crawled up and over obstacles others flogged it, spun the tires, chewed them up, bounced around, slammed trees and put on speed to try to make it the first try.
I just locked up, crawled and let the H3 do it's thing, I have a winch!
Can I have an amen brother Hummer owners??? I'm preaching to the choir, amen Hum on..............
and I drove mine over there and home, whilst in comfort with the AC on and Satellite radio playing the layed back 70's
sorry I tried to keep it down to no scrolling.
This is one of those situations showing an H3 doing it's thing, but you can see the front end ground contact is not very much.
I plan to run the spare behind the front row seats, when I'm wheeling alone. If your vehicle does start bouncing back off ASAP. That's because it's the best way to break cvs. 
