Wilbur is a simple 2D paint program that has some weird bits and pieces that lets it pretend to do things that it's not really qualified for. It's also broken
The simplest way to get rid of pole pinching with widely-available tools is to paint your polar map areas on an appropriate projection (like an equal-area polar projection), use a tool to unproject the newly-painted map to equirectangular, and then assemble the pieces together. The most correct way, of course, would be to use a paint tool that is aware of projections and warps the brush so that it's the correct shape onscreen, but Wilbur ain't one of those. If you use Wilbur, you get to spend a lot of time pretending (pretending that the bugs aren't too bad and that the developer will get around to fixing them, for the most part).
There are a number of reprojection tools out there to go from one projection or another to equirectangular, but a simple one is http://www.fracterra.com/ReprojectImage.zip (the same place you got Wilbur). It unfortunately only works with 8-bit images and can be a bit twitchy to work with, but that's often the price of free software.