No, setting fuel height doesn't require a re-synch. However, once the carbs are properly tuned (AF, jets, etc...) a final vacuum synch may help if you don't get them running right. Also, remember that your valves need to be adjusted properly before a synch (I think that was an earlier post).
Yes, the insufficient fuel issue will be attributed to ALL your stumbling, lean, loss of power issues. Not the only issue, but a major factor. You now see why setting floats by mechanical measure simply is not suitable enough to be accurate. Its a good start, but unless you're skilled it, have the carbs mounted on a bench and sitting perpendicular, you are bound to get variances.
