In this specific case, write a new answer
I found two pretty polarizing cases from Meta.SE. One, Is it OK to write a new answer after I deleted a downvoted one earlier on? is answered with:
Yes, definitely write a new answer.
While another, Deleting a bad answer & posting new vs editing, is answered with:
No, by all means that is the last thing you should do.
Here's what I see as the big difference between the two. In the first, the OP is thinking of answering the question with a completely different answer. Ideally, there is no (or minimal) overlap with their previous, downvoted answer.
While in the latter, OP doesn't really specify. The assumption is made by the answerer that they know how to improve the answer, but the core of the answer would stay the same--that their core advice would not change.
And this makes sense, right? If you have a distinctly different answer, then it deserves to be posted as...well..a distinctly different answer. But if all you want to do is modify how you're delivering the same advice, or add some personal experience/interesting articles/or additional advice for different ways this can play out, well...that sounds like an edit to me.
But at the end of the day, if you think your post is distinct enough to be a different answer, go for it. And if it's not, the mods and community members who can see deleted answers will flag/remove the new one and let you know.