Being a certified electroplater I think I can help you and I still seem to remember a little chemistry. Spatulas held relatively small amounts of materials, maybe .10 - .20 grams. But I think the point is that it doesn't require much zinc oxide for this to work on a small scale.
As I recall, a good working alkaline zincate bath needs only 80-100 grams/liter of zinc oxide added to 400-500 grams/liter sodium hydroxide to deposit fairly efficiently. Heating the bath probably accelerates the zinc reduction on the copper coin, but at 25°C, the reaction should be immediate.
Hope that helps.
