The general idea of the site is that posts are not static but can change over time, and indeed should change over time when it makes an improvement.
Thus, in principle there is not only nothing wrong with changing an answer, it is even desirable to do so under certain circumstances. As pointed out in the question-post there is, however, a concern about continuity of the ideas presented, as the votes and especially an acceptance convey some information and it thus might not be good to change too much.
In particular, a questioner might be unhappy if the answer they had accepted, then says something completely different and it still seems they have accepted it, while they might not like the new answer. However, this problem is mitigated by the fact that they could undo the acceptance if they so chose. The same is true for votes; following an edit of a post even old votes can be changed.
Thus, I my mind as long as there is some continuity of the ideas, editing is fine. To be sure, this continuity can also take the form: "Earlier I thought {roughly that} (see revision for details), but now I do not anymore because of {something}. But instead I believe {this}."
If the envisioned new and old version should however be completely independent it seems more natural to me to create a new post and possibly to delete the old one. For general considerations on when to delete an answer see a recent meta thread: When should a person consider deleting an answer?
On the technicality of not being able to delete an accepted answer: to get around this, one could flag the post as "other" with the deletion request and a moderator could still delete it. In theory, it is also possible to disassociate a post from a profile, preserving the post but still removing any link to the user that created it (the post will appear as if it were from a delete "anon" user); this however intended as so rare and unusual that it is something per-site moderators cannot do, and it needs to go through SE. Thus, this should be reserved for truly exceptional cases (mainly for questions, where deletion has implications for the answers).
To sum this up: as long as there is some continuity, even if only vague and indirect, I think editing a post is fine. However, if the situation would be such that the old post-box is just cleansed entirely to then be used for something completely different, then I think creating a new post instead is preferable.
In case a strongly edited post is an accepted answer it could make sense to notify the questioner (for example, via a comment on the question-post) so that they can see if they want to change their mind on the acceptance. [I believe edits to answers do not notify the questioner and if it is an old post they might well not notice, whence this suggestion.]