Can someone confess to a murder after being acquitted?

I would think the answer to the question in the OP is that it would be exceedingly risky to do so. The site that I cited indicates that general principles aren’t all that firm in this area and each case presents a unique opportunity for courts to allow prosecution on at least some charge or other if not the original one.

“I didn’t kill my wife, but if I had, it would have been because I loved her very much.”

Sounds like a confession to me.