Air filter or air box, both would restrict the amount of air going to the carb, which richens the mixture, particularly at high revs, and yes, an airbox would probably be more restrictive.

I suspect your problems will be with the main jet rather than the adjustable idle jet. Some can be adjusted by lifting the needle higher in the carb slide, but you may need a bigger main jet, this is what I meant about it being a lot easier to just blow out the old carb's jets. You know the old carb worked right before dirt/water got in, so it will work right once you get water/dirt out.

 

Going to try old one after a good clean. But any chance do you no a site to get a Manuel ?