If you can improve an existing post while respecting the original author's intent, you should make (or propose) that change via an edit. As question author, you have a little extra "moral authority", in my view.
More generally, if the answer is genuinely Not An Answer, but could be made so with an edit, consider doing that as well. The best action in each case is highly context-dependent.
If your edit is rejected or rolled back, you also have the option of asking and answering a separate question to preserve the useful content.
In this case, I think the new contribution is a good contribution to the accepted answer, so I have made an edit to incorporate it. The post owner may choose to improve, accept, or reject my edit as usual.
I also left a comment for the author of the improvement, before deleting their answer: