Black smoke = flooded engine.
If it were lean, there would be nothing to burn black, and you would have to pump the heck out of the gas to get it to restart.
You are flooding out the carb on a steep grade. The car will start and run like normal at the bottom, because the level of fuel in the float bowl is correct because you started on level ground. As you go up the steep grade the float level changes from the angle, dropping the float letting in more fuel than normal. Also, the float vent is in line with the car with that carb(I think), dumping fuel down the throat of the carb when it is at weird angles.
Unfortunately, that is just the nature of the beast. You can try dropping the float level, or perhaps extending the bowl vent higher. But, if you want an all angle engine, you need to get rid of the carter carb. Some people have luck with edelbrock carbs. An expensive EFI kit will fix it right up, but it is... Expensive. You might be able to get around it by down shifting and letting the engine rev higher, but if you are already in first and lugging that won't work.
If you have a good set of dial indicators and torque wrenches, I'd go with an old fashion detroit locker in the rear. They are strong and reliable. If you still street the jeep, you may only want just a rear locker. I still like my lockrite though. It is simple and works for me. When it breaks or wears out, I'll probably get another. All you have to do is pull the diff cover, yank out the old side and idler gears and replaces them with the locker. It isn't as strong, but it is so much cheeper and so fast and easy to install that the weakness is outweighed in my mind.
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