I had one of those hinged omelet pans once ... it was easier to just learn to do it right with a skillet and spatula than to mess with that thing.
Something you might try ... technique I think I learned from Julia Child for something like this:
After the bottom is browned and the top is set, use a spatula to make sure your kugel is not stuck and slides easily in the pan - then, invert a plate (or a pizza peel, etc.) over the skillet and quickly, but carefully, flip them over. Regrease your skillet and then carefully slide your kugel back into the skillet to brown the other side.
This what I do with frittatas.
Hope this helps ....