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...).

Oh, that's brilliant! I'd seen this described before, but not distilled down to that specific order. Thank you!

It does bloody work as is. People bloody say "bloody verb" all the bloody time.

Here's a bloody example: https://www.youtube.com/watch?v=OGWhjojt5dw

Probably just because you're not familiar with the usage.