Is there any kind of adjustment screw in that new carb? Also, make sure your air filter is clean, might throw off your mix at idle.
I do agree with the new carb when you find one cheap enough. However... In case u are in a jam for time (waiting a few days for part to arrive) or you simply like to tinker, here are a few thoughts.
In the days before fuel injection and fuel maps my bikes were carbureted, and since I had no kids and nothing really "useful" to do with my spare time I used to tinker. At least once per year I did a complete carb tear down to meticulously clean every nook and cranny. even tiny little things will make a difference, and the smaller the parts the worst it gets. Then (in multiple carb engines, not really your case) you need to tune them and balance them. On one bike I had to replace all needles and jets to compensate for the new full exhaust system, custom air box, intake, hotter ignition harness and coil. Since there are really multiple combinations there was plenty of trial and error to find the smoothest setting, You might have a great pull on low end, but weak on top, or a rough idle.
You case seems to be mostly gunk accumulated overall. You need to absolutely clean everything including the float. The added weigh of any type of gunk will throw it off.
Replacing everything is much simpler, and if you go that route definitely order a whole carb vs rebuild kits. Remember that when rebuilding you are "mating" new parts to worn out "carb bodies", it will never be as good as a full replacement or as easy. But for the "tinkerers" that will always be the last resort,
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good luck