The Jeep is short wheel base with solid axles in the rear AND the front. I think it is just the nature of the beast. The Wrangler does not ride, or drive, like any other 4x4. I know what the OP is saying, but I don't think it is a symptom of a problem.

 

As I said, overall, I find the suspension very good, and made even better with the air springs.
After some 7 month of daily 'Jeeping', on & off road, I can say that I never enjoyed any other 4x4 which I had as much as I enjoy this Jeep.

Is it 'perfect'? No.
The automatic transmission, for instance, should have had at least one more gear by 2010 (my JKU).
The solid axles shouldn't have transferred that slow speed jolt. This too, could and should have been solved by now, by changing the geometry, not the axles.

Both things are minor, compared to the rest of what a Jeep is, and capable of doing.
I just wondered if there's a solution for that jolt, and it seems there isn't.

 

Everything is a give and take. I find the JK ride feels very similar to a modern HD truck with live axle (ford or dodge) except rear springs feel much softer. I believe the harsh jolt at low speed is inherent to live axle, boxed frame design. The live axle design has a huge disadvantage compared to independent suspension due to the large unsprung weight of the axle.

The easiest and cheapest way to combat this is with tires. I do however believe that the control arm geometry could be designed to minimize this jolt by changing the length and attachment points of the control arms on both the axle and frame. This would likely come at the cost to ride and performance in other situations. For example, all things equal, the lower the frame attachment points and the more horizontal the control arms the less jolt. Even better would be if the control arms attached higher on the axle than on the frame. This obviously is not a consideration on a jeep due to packaging reasons.

 

We aren't as lucky as you are in the US, as going wild with tire size is illegal here.
The factory 245x75/17 (31.5") will be replaced in a few days.
My choice would probably be the BFGoodrich Rugged Terrain 285x70/17 (33").
My wheeling doesn't include deep mud, and from what I've seen on others' Jeeps, they seem to be very capable w/o loosing road behavior.
With a little bit less pressure, they're supposed to soften those jolts as well.

I also still wait for a test drive with Full Traction long arms on a JKU... probably in 10 days or so.
It would be interesting to feel how they influence the ride.