The OP has a V8 or so he says. There's NO 2H. He's in 4H-AWD all the time.
When I hit the bigger snow in my V8, I usually have no problem with the regular 4H (AWD) setting.
If the traction control kicks in too much, I lock the center differential and now I have 4WD. But I only drive this way on wet or snowy roads. It does not like or should be driven on dry roads this way.
The 4H-AWD 'normal' setting on the V8 is excellent for most driving in snows. I wish I had a deactivate setting/button for VSC/Traction control.
Thanks for catching that; I missed the fact that he has a V8, even though it's right there in the title.
The information is still pertinent. A V8 is always in H4, but the three differentials are still open until the center is locked. It's the same system as the V6, albeit without the option of 2H.
The OP was feeling dissatisfied with the 4Runner's traction capabilities compared to his previous Pathfinder, so I think it's important to explain the versatility of the 4Runners 4X4 system.
Everybody is claiming that their 4Runner in 4H (unlocked) does just fine in snowy conditions. Everything else being equal (tires, clearance, and so forth), an AWD vehicle with three open differentials will have better traction than a front wheel drive vehicle, which will in turn have better traction than a rear-wheel drive vehicle. With that said, I think the value and utility of locking the center diff is downplayed. Point in case: a front wheel drive vehicle will not get stuck with a rear tire spinning, whereas our 4Runner can. The off-roading crowd knows the value of a locked differential (regardless of where the diff is, and those crazy bastards will put a locker on everything), and having three open differentials is not conducive to traction on a slippery surface. If this is true off-road, it is certainly true on-road (when the road is slick with ice, compacted snow, or piled snow).
The 4Runner owner's manual explains that 4H (whether for V6 or V8) is good for general traction on all road surfaces and can be used at all times. It then states reasons to lock the center differential: if greater traction is needed, if tire slippage is occurring, and/or if the VSC is cutting the throttle due to tire slippage. These scenarios are exactly the problems the OP was facing.
Turning off the VSC with three open differentials would only further hinder traction. There's a reason why the stability control cuts throttle when a tire is spinning when all three differentials are open, and a reason it turns off VSC with the center locked. We may not like it, and we may not like the feeling of it, but if it didn't cut the throttle, then the extra torque from pressing the throttle would just be sent to the slipping tire. With three open diffs, one cannot just "power" through a spinning tire. Conversely, once the center is locked, even if a tire is spinning (and therefore robbing traction from the other tire on the same axle), the two other tires on the opposite axle are still getting torque (as there is no center differential to redirect torque between the two axles). Thus, one can "power through" tire slippage with the center locked.