A fictional world is probably easier. Or, if you want to use a Europe map or something, just go total alt-history and create the kind of background you need. I know you tried to do that with the Black Death thing, but:
a) That's too similar to real life, some people will go on and on about people not being 'historically accurate' even if it's not supposed to be.
b) If this point of divergence occurred, there would be a substantial possibility for an invasion of a severely weakened Europe by Islamic nations from Africa and the Middle East, and probably the Mongols from the East as well. And the Vikings survived relatively unscathed IRL (relatively, they were hit by it like most others), so there's the potential for a northern invasion. I don't see any low-tech level new city states racked by plague surviving in the face of threats from three cardinal directions. The book, 'The Years of Rice and Salt' by Kim Stanley Robinson explores such a scenario from a global perspective.

As you can likely tell, I am one of those in danger of falling into the trap of point A :)