There are a couple of things that need to be covered here, as all of the info is not present. You said you rebuilt the BB set. If that means using the same cup, spindle and balls that may be the problem. The most critical part of an overhaul is inspection and we do not know if you did that properly.

The cups and spindle cones should be smoothly worn with absolutely no pits and the track worn by the bearings should be fairly even in width. If that is not the case then I would replace at least the components that don't meet that criteria, and in most cases the entire unit. As for the ball bearings I would NEVER reuse the same ones as they are impossible to inspect for defects and are considered sacrificial. In addition there is no reason to stay with the bearing retainer, unless you can't manage a loose ball reassembly and the cage is one of the higher quality ones that uses a full complement of 11 balls on each side. The more balls there are the less stress any one has to take and the more even will be the wear.

If the bearing surfaces pass the criteria above the odds are you can achieve a no-play adjustment that is also smooth. I agree no play is best, as the knock/impact each time you do a stroke will quickly cause problems. If you replace with a new cup/spindle set you should still go for no play for the same reason, and then check often for readjustment, as the balls will soon polish a smooth run on the new surfaces, removing a small amount of material in the process. Except for high end equipment new bearing parts always run a bit rough initially, although there should be no "catching."