Requesting a core profile without a version doesn't make sense to me. Since newer versions can deprecate old functionality, it would be possible for you to get a much newer core version that disables some functionality GZDoom uses. Specifying a version would tell the driver what functionality you need, and can then provide the best GL version that it can give that functionality with.
I can play around with requesting core profiles. But since I'm not too familiar with doing that (haven't really directly used core OpenGL stuff much), and I don't have an affected system, other people will have to test any patches to see if it fixes this issue without breaking anything.