What oil filter do you use? I use the black Subaru/Roki "160" filters, and I've never had one leak when I remove it. As with your process, I always drain the oil before removing the filter.
Before I remove my drain plug, I remove the oil fill cap on top of the engine so that the opening will allow air to flow into the engine, which speeds draining.
But I can't imagine that this has anything to do with your filter drainage problem.