Well, basically speaking it's the same premise than your story (at least as it looks like so far, because there's still place for possible twists):
Peoples are put in cryo during their travel to Mars, and something goes from, interfering with one of the simulations. The person in that simulation wanted to be a cop in the 00's, and suddenly after some time like that, he become a cop in the 70's and try to understand what is happening to him.
Your English isn't bad (at least to my eyes), you could do the translation by yourself.
Like you pass over it once, I'm not sure that it would really need more times that your current process. And it would make you catch more surely confusions like "Kiss Wendy" and "Fuck Wendy".
Saint Blackmoor shame on you for the him/her
More seriously, it explain why the literal part of the translation is limited to some specific cases that are confusing in the intent more than in the meaning. If I find some time, and achieve to get rid of my near to burnout state before the end of the holidays, I'll jump on it to catch those cases ; no promise.
They do so in English. After all, it's the base of slang, whatever the language. Reason why I said that the issue is the literal side of some translation. Beyond this, the English is more than correct.
You should have more confidence in your English skills. I'm far to be the best person to judge it, but I never had issue to understand your posts, and I'm sure that I'm not the only one.