My recommendations based on it's function and my experience:
Things to avoid.
1. Avoid getting into situations where you need to switch into 4wd while your sitting still 'Stopped', AND will need all 4 wheels to pull at the same time. Such as stopping halfway up an ice covered hill to shift into 4wd.
In this situation, the rear wheels will brake loose first, and likely spin half a turn or so before the front wheels engage. And the front wheels will engage quickly, probably spinning a little too.
Activate the 4wd at the bottom, and the application of power combided with the flexure modulus of the tires will have all 4 engaged and pulling before you even get to the hill.
2. Avoid areas where you'll need to go back and forth between forward and reverse without wheelslip. When you switch from forward to reverse you'll need double the wheelslip to engage the system. Then, when you switch back to forward, you'll need double the wheelslip again. Sucks if you need to rock back and forth.
3. Avoid sudden high speed engagement of the 4wd . This isn't likely to be a problem, unless you get your driving advice from the internet. The traction control will prevent damage, unless you've turned it off.
Example situation that could cause this: While stopped, you turn off traction control, engage 4 auto, then hit the gas. You'll immediately get high velocity wheelspin in the rear wheels, and the computer will power the ballramp mechanism, which will hammer the front wheels into engagement with a violent shock load.
If the traction control is ON, it will detect the high velocity wheelspin and reduce power before engaging the ballramp.
Things to do:
Turn on 4wd early. Once the rear wheels have turned a few times and the ball ramp has engaged, it'll stay engaged as long as your applying some power.
Don't be afraid to trust the stability control and traction control. Contrary to internet lore, it makes things better, not worse. The only time it's a net negative is when high speed eheelspin is needed to centrifugally spin mud out of the m/t tires lugs.
Don't try to outsmart the computer. It's programmed to start/stop actions based on sensory inputs. If your doing something the programmers couldn't forsee, the computer and traction control will behave in unpredictable ways.
Example: you put your truck on ice, and shift into 4 low to show everyone how bad your 44-44 sucks. You get out to film your rear wheels turning while the front wheels are stationary.
In this situation, the following occurs, cyclically, in fractions of a second. The rear wheels start to rotate, the ballramp electromagnet is energized, and the rear wheels start to rotate, depending on how slick the ice is under the front wheels, they may start to spin too, The stability control interprets this and wheelspin and begins selectively braking both the front the rear wheels (which causes the ballramp to begin clocking back and forth, and stop compressing the clutches, just making a nasty ass grinding noise), the wheels stop and the abs stops braking, then the wheels start rotating again, then the ballramp engages, then the abs kicks in again, then the ballramp releases, then the abs releases, then the wheels rotate, then the ballramp engages. The cycle repeats, multiple times per second, over and over, generating heat, wear and possibly damage. The exact timing, force and results of this cycle will depend on relative friction under each wheel, condition of the clutch friction plates, and the idle power transferred by your torque converter.
Don't: Test the 4wd by holding the brake and throttle at the same time. It creates a lot of stress on driveline systems, AND if you do happen to accomplish your goal of getting the rear wheels to spin, your ABS and stability control will interpret this as wheelspin and begin doing strange things, as well as reducing power. Also, while the ABS is modulating the pressure in the brake lines, the ballramp will be rapidly engaging and disengaging (picture the ballramp plate driving the front sitting motionless as the other plate is hammering back and forth), as the ABS is selectively modulating the right and left, front and rear brakes independently, reducing/adding power, and trying to figure out WTF is going on.
If you really want to test this system, here is how to do it:
leave the truck in 2wd, leave the traction control alone. back into some deep mud, snow or ice and get the rear wheels really dug in and stuck good. Stuck good enough that in 2wd, you cant get out but not so deep that the front wheels cant get you out. Leave the front wheels on some nice, dry, high traction surface. Or, put the rear wheels on a set of roller dollys, while leaving the front wheels on pavement.
Now, put it in 4 lock or 4 auto, and give it some gas. The instant the rear wheels slip, the traction control will slow things down to prevent it from engaging too violently, the ballramp will transfer all (100%) (the rear wheels will still be turning, but this doesn't count as torque since they aren't pushing against anything), of the engines torque to the front wheels and all questions and mysteries will be answered. The Hemi, and that 44-44 will yank your ass out of that mud so fast you won't believe what happened. All 410 ft lbs of torque will be applied to that contact patch of rubber between the front tires and the road surface.
When I started seeing all the internet complaints about the 44-44, this is the first test I did. I went over to Canyon Creek Road, just east of Glacier, WA near Mt Baker and stuck the back wheels in a couple feet of snow, with the front wheels on some pavement. I left my first -front wheel only- black mark. When all 4 wheels are spinning, the ECS will allow you to apply all the power you want.
Don't believe me? Before you respond and tell me how wrong I am, go find a muddy ditch.
I drive a 2012 Chevy Tahoe for 8 hours a day, 5 days a week, and my Ram Sport the other 2 days, in the Cascade mountains. The Tahoe has the 44-05, which is smaller but otherwise identical to our 44-44. It behaves the same way.
I get that Tahoe stuck plenty, since someone else owns it, i'm a lot braver in it. Above the snowline I have plenty of opportunities to stick the rear wheels in 2wd, then pull out with the front in 4 auto.
Where the 44-44 and the 44-05 both really work well is climbing really steep, loose packed rocky mountain roads. There are tons and tons of time when all 4 wheels are spinning at the same time, and the ballramp stays engaged, all 4 wheels keep powering on. The hardpack level switchbacks are easy, because you can make steep, 180+ degree turns without dragging or binding, and when you start climbing again, all 4 wheels are pulling again. In this application, the traction control works like anti-spin diff, when a wheel spins over a rock or spins out climbing loose gravel, the TC brakes it and moves power to the other wheel pretty seamlessly.