The "even" both breaks up the flow and makes the "bloody" unnecessary - i.e. you've already said "even", you don't need to say "bloody" too.

So although there's nothing grammatically wrong with the sentence, it reads awkwardly. A native British English speaker would be more likely to use your suggestion. It's just one of those barely documented curiosities like adjective order (https://www.theguardian.com/commentisfree/2016/sep/13/senten...).