The key to getting it to not pool is to be constantly rotating the object while waiting for the paint/ink/dye to catch and hold. It's annoying but it really works to get a nice smooth coating. At least, that's how it works when pouring something inside the hemisphere - any product that has to be swished around inside it has to be kept in motion until it genuinely starts to dry, in which case the best product is the one that dries the fastest. The dye methods might actually involve dipping the whole piece into the dye, so that would be different. Either way, when I did it I sat there watching TV while slowly rotating a plastic cup in my hand until the paint started to dry, and then set it upside down so that if any remaining paint pooled off, it pooled to the edges, not the center.
Peeling glue sounds fun though.