Burning oil transmission

It shouldn't be a problem going down hill, the automis hardly working then. Is it the oil leak you had previously spewing oil onto the exhaust. If there was smoke from the auto itself, then I think you wouldn't get far as it will soon fail if that is true. Having the oil professionally replaced means what exactly.
Don't you wash off spilled oil from engine and vehicle??? And have you washed of the previous oil being distributed all over the lower front.

Not the transfer case draining back into the box? Haven’t heard of that in a few years. In low range the auto box does bugger all work.

Damian
If you own the vehicle then you can investigate where ANY oil leak is originating from. I doubt the oil is burning, that means flame, heated so it smokes is a bit different. Usually only the exhaust pipe is hot enough to do that, so some oil may be dripping into it. Did you fix the previous flood of leaks? Engine oil smell and trans oil have different smoke odours, so maybe a bit of heating some of both will clue you into what is happening.
When you say "driving hard" exactly what does that mean? Driving in difficult terrain or going fast as in driving it hard flat out?

When you give the initial clues, maybe try and include more observations, when, where, how often, etc, to enable, at least some targeted replies. When the story changes the original replies then become obsolete and the original comments are then often invalid or not focused on what the problem may be.