You can try lowering the float level in the carb. It will help but might cause it to run lean on level ground. That is the problem with carbs and jeeps, carbs don't like changes in inclination, and jeeps love them.

How much money do you have to spend on lockers? Do you have good mechanical skills and tools?

If you have no money and no mechanical skills, a lockrite or similar product is the way to go for the rear axle. I've had a lockrite in my jeep for 4 years now and it still works great. Otherwise if you have money, the sky is the limit. ARB's front and rear, ETC...