For what it's worth, I've never had much luck rebuilding carbs. I've been able to take them apart, and put them back together with the new parts, but they never seem to be much better after I finish than before I started.
It's hard to find exactly the right kit for these old ones. Generally you end up with one that is supposed to work with several different models, and then you're not really sure if you have the right parts, or which ones you should use in the kit.
I think the problem is that they are old, everything is worn and loose and the parts you replace don't correct all the problems.
Also it is hard to get everything adjusted properly. For example: You mentioned the float. Maybe someone can give you some advice on how to do that properly, but with me it is always hit or miss, guess at it, and hope it is right. Unless money is a real consideration I would recommend using your old one for a core, and getting a factory rebuilt one.
I'm not sure, but I think there are new 2 barrels that you can get, which should help everything.
Probably a lot of people will disagree with me. I'd be interested in hearing other opinions. Allen