How do I acquire the skill of not cringing at my voice when I record it and play it back?
Do it more. I'm sorry but this is truly the only way. You just have to kinda normalize the perceived difference between your in-head voice and recorded voice through exposure. You'll get to a point where they sound the same (or at least the differences become so expected as to not really trigger a response) and you have an overall consistent picture of what your voice sounds like.

















