If an overflow gasket does not fit, can it be rotated?
I would replace the rubber gasket you have with a more pliable foam-rubber replacement (commonly available at plumbing shops). This should allow you to place the gasket in the normal position (thick at bottom) but to give it a squeeze to effect a seal all the way around.

In the end, it is the seal at the bottom that is most important. Why? Because any water that gets to the overflow under normal circumstances is just incidental splashing and not likely to cause a huge problem. In the worst case (actual high water level, the reason for the overflow port), large amounts of water will be flowing through the bottom part of the hole. Any gap there will result in floor/wall/home flooding and damage.