For the dot pattern you could try and use the same stuff people use for lenses, maybe a computer fan filter replacement would work for what your trying to do. I don't think you want to screen print the webbing in puff paint the best thing to do would be hand draw the lines using a pen on the unsewn pattern and then puff paint over them. Its a lot cheaper this way then screen printing.
This is just an idea, but my experience with puff paint has never been fun. It isn't self-leveling and it's hard to control. Perhaps you could try using a stream of hot-glue in place of the puff paint and paint over it to get the color you want. Hot glue is fairly self-leveling, though if you are looking for a thin line I would suggest using a low-temp, mini hot glue gun. The low temp will dry much quicker, which will still self-level but not flatten and a mini glue gun will give you a thinner line. This might require some testing to get a feel for the consistency and motion to get the desired product. Just an idea