There is not a lot of love for the Carter BBD or even worse the Carter YF carburetors around here

They're notoriously crappy carbs that require constant attention.
Instead of trying to mess with it, it may be simpler to just replace it, there are lots of remanufactured options available from Summit Racing or any other online retailer for around $200 with a core charge. There are also Holley sniper BBD direct replacements, but they run about $1,200. BUT, if you go fuel injected, you're going to have to drop your fuel tank, install an electric fuel pump and get rid of all of the stock rubber fuel hose, so the $1,200 is just the starting point.
There are also kits from Weber that are direct replacement for the BBD;
http://www.redlineweber.com/carb-kits/auto/jeep/
IF you're thinking about swapping to an Autolite/Motorcraft 2100 series carb, which a lot of us have done, there is homework you need to do. It is NOT plug and play, throttle linkage is different, vacuum routing is different, your stock air cleaner won't fit, just to name a few of the common problems.
Let us know what you decide to do, we're here to help if you need us!