The demise of the Roman Republic was an inevitability. It could have been Sulla rather than Caesar, and if not Caesar it could have been another, but one way or the other the situation was fundamentally unstable and the public was deeply discontent. Would be reformers like the Gracchi were finding enormous popular traction only to get assassinated.

Also, the Roman Republic were prolific slavers too. I say this because you speak of the Empire and slavery but then go into a "But the Republic.." This isn't Star Wars, you can't divide it into good guys and bad guys, the Republic and Empire were both imperial sons of bitches who conquered territory and took civilians as slaves. The demand for reform that would eventually motivate mass conversions to Christianity was already well established before Caesar was even born.