Some basic checks:
Was the engine and governor working fine before you replaced the carb? Why did you replace the carb?
With the engine off looking into the carb throat, does the butterfly move from closed to open when you move the throttle from off to max?
Does the governor arm move freely when the engine is off?
Does the governor arm move at all when you rev the engine? If not then the arm may be rust frozen, slipping, or the internal gears may be stripped and you’re hosed.
If the governor arm is moving when the engine is rev’ed you may need adjustment. That is, if it’s really moving correctly and you do not have another problem.
You have been adjusting but could it be that the governor arm is adjusted such that it’s closing the butterfly when its rest position? That would make it that it will restrict gas on startup and try to restrict gas more after start and the throttle is increased.
If the butterfly responds correctly when you move the throttle from off to max and the governor arm moves when you rev the engine then you probably need adjustment…provided…its not something else unrelated to the governor which can be addressed when the above checks are done.