A system that uses only thrust bearings and needle bearings will have play unless all the space inside is taken up on installation. I would try cleaning, regreasing, and reassembling, first. Needle bearings are not typically pressed into place, unless they are part of a cartridge, and the race is pressed in. A firm push should dislodge them from the cups.

FWIW, thrust bearings and needle bearings in your application would be unlikely to wear excessively from use, more likely corrosion. If you had a micrometer, you could measure the wear area for any appreciable difference as opposed to the unworn spots.