On the TCI bikes the TCI box doesn't like low voltage. If it drops much below 12 volts the TCI can't function as it should. Resulting in running issues you describe. It can also be a weak magnet in the rotor.
You can do an easy check for both of these issues by fully charging the battery then unplugging the reg/rec. This stops the power flow trough the rotor. Allowing full battery voltage to the TCI as well as letting the pick ups read the magnet better.
If it runs well with the reg/rec unplugged then you need to check out the charging system to ensure the TCI gets the voltage it needs.
Once you get the charging system working right that may take care of your running issues.
If not then you can check the strength of the rotor magnet. Try sticking something steel on it and see how hard it comes off. If it's easy to pull off the magnet may be weak.
On your carbs, did you buy a kit with jets and such in it? Most kits don't come with the right jets and such with them.
Myself and others don't recommend kits fort his reason. Follow the carb guide to tear down, clean, inspect your carbs. Once you determine what needs replacement just buy what you need. Most of the internal parts and if careful even gaskets can be reused.
When cleaning pay particular attention to the idle circuits. They have small passages and tiny ports that plug easily. and are hard to get clean.
Leo