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Stefan, that piece of paper seems to be approximately 10 cm2 and you are getting 2.1 ma. the air electrode at the same size would produce 3 amps. I think the acrylic binder has to much resistance and will only work when submerged in the electrolyte. When submerged, there is a limited supply of O2 therefore current will always be low. I also tried the acrylic binder as an air electrode binder and found that it would not work. Try using a piece of copper the same size as your paper and the current will be around 500 ma.

Also, I have had better results with bleach electrolyte when using aluminum. The copper will not be consumed.

Wiki says that zinc-air batteries give off energy as the zinc oxidizes. And that they stop giving energy once the zinc is fully oxidized.