Hmmm, that does sound difficult. I wouldn't write anything untrue, not genuine or in any way not resonating with all of you. Honestly, it sounds to me like he should be the one to reach out or at least apologize if and when you do. He caused you much pain and then goes on to blame you for the state of the relationship between you? What a dickhead. That being said, if it resonates with you (no worries if it doesn't), I'd keep it simple, no more than 5 sentences. Something like "hi dad, I've been thinking about ... (e.g. life) ... and would like to give our relationship another chance. Let me know what you think."
Something like that. It doesn't cost you too much effort, you ideally avoid investing much emotion into it and the accompanying devestation if there is no or no positive answer.

You know, I think I might just go with "solo sex" when it comes up. I do strew in some english words here and there and T adapts to them fine. Thanks for giving me the gift of language