Has anyone tried to install an upgraded oil cooling kit (like Stillen) to help reduce the oil burn associated with the 3.5? Question 2: would this even help?

Thanks in advance

I don't see how this would help the issue at all.

new engine time

lol not even close George, but thanks for the troll

Cooler Oil= Less Burn? Does it work that way?

No it doesn't. Oil burns when it enters the combustion chamber; whether it be through the intake port (PCV), piston rings, or the valve stem seals.

Then accept it and top it off occasionally

Dumb question but the stock oil cooler is air cooled and has a thermostat in it correct?

The stock oil cooler is water cooled and does not have a thermostat in it. It is the unit that your oil filter screws on to.

Yes^^^

Coolant flows thru a device (essentially a heat exchanger) where the filter mounts to the engine and it's designed to carry excess heat away.

The stock system is not like an auxiliary set up with oil lines running to a mini-radiator

K. I like those.
My 3.0 doesn't have one maybe I'll steal one from a junkyard 3.5.
Will just screw on right?

You will need the hardlines and thermostat as well.