I've seen kits with and without the spring,
A worn fatigued spring will have the same affect as raising the fulcrum arm and richen the mixture across the board. In my experience its not a problem re-using the spring, as its unlikely its so fatigued it wont provide adequate pressure to seal the needle and prevent flooding. The needle and seat condition is way more critical to proper function. Make sure the fork in the fulcrum arm isnt bent (both tangs parralel) as this will cause the needle to bind and flooding/ erratic running.
Set the arm flush and that should work fine. Higher arm setting will generally richen the mixture necessitating turning in the H and L needles. Too low a setting will do the opposite, and needles will have to be opened to compensate. Needles will compensate for any small variation in arm height and tired springs etc