Many, if not most, of the leaders in science, art and exploration (at least in the western world) in the middle ages were Islamic
News to me. I recall a geometric math... thing, invented/discovered by Moslims "back in the days", but the westworld seem to have been more influenced by its state religion christianity when it comes to art and scientific development. As for exploration, I can't say.
But now, to the point.
Imagine another universe where Martin Luther King Jr. led Germany in the 1930s and 40s, and Adolf Hitler led the civil rights movement in the 1960s. Playing a game like Free Orion is the same way. Your playing basically infinite variation on the same universe. Why can't the races you play against (or even with) have the same variation?
This is where my suggestion of culture components works just nicely. The player or AI either get to make their picks before the game, or start with a random set of components, and have to mold their culture into what they prefer.
What this means is a random culture for each race, your get those infinite variations of it. Even more so if the results of changing from one component to another has a specific effect on the civ. For example, moving from a theistic to an atheistic view could result in scientific boosts but just as well lead to scientific stagnation; health bonus from the lack of stress associated with sacrifice and/or good deeds, or health penalty for the lack of afterlife to hope and strive for.
If the results of cultural change also has a random factor involved, you can't just rely on memory to figure out what component you can change into another, there's an element of luck involved as well, and the strategy comes in at when you can change without suffering penalties in the middle of war.