Dropping the needle will primarily affect the mid range response .... if that wasn't wrong, it should then produce a flat spot as the throttle opening transitions from low speed into that range.
In effect, you'd be moving the two parts further alway from each other as it'll not change (much) the lowest point metering. Low would stay rich and mid would move toward lean.
If it's definitely rich at low slide opening, then it's usually the idle jets (assuming the others aren't nuts in volume) and so you'd correct with them by going smaller idles.
Of interest, what absolute vacuum reading is shown on the sync gauges if you use them ?
This complexity is why I'd be absolutely sure of cam timing before you begin diagnostics of carbs. If wrong, it'll run you ragged trying to think what you can adjust or the permutations of error ... all in vain too.