This isn't an answer to your question but I've seen a few JL/JTs on steep inclines (35%+) start to smoke oil if they get hung up or are at that steep angle for too long (I'd say at least 30 seconds but probably even longer). I've heard that it's from oil getting into the PCV valve and fed into the intake causing the engine to burn the oil. I would assume that means that oil is still being pumped from the oil pan at those steep angles..... but I'd love to have someone verify that (or tell me I'm wrong).
FWIW, Teraflex makes a kit to keep the oil out of the PCV on steep inclines. Does not cure the oil tube pickup starving problem but will keep the oil from getting into the PCV.
I installed a UPR oil catch can
It does three things
1. Keeps oil from being sucked into the intake at steep angles
2. separates the oil mist from the PVC system keeping the oil mist it from entering the intake manifold
3. greatly reduces the carbon build up in the combustion chamber leading to pinging / detonation / spark knock
Before I installed the catch can my 3.6 it would ping / detonate under the slightest loads
After the catch can NO more pining / detonation
I was amazed and shocked at how much oil it collected after 1000 miles
There is a drain plug in the bottom of the catch can and I added a 4ft 1/2in. drain hose that runs to a lower part of the jeep and now every 1000 miles just open the valve and let it drains
This doubled its capacity and I no longer see any oil in the can. Its all in the hose
I was skeptical at first put now convinced