Several years ago, there was a post on this site that probably answers your question. Unfortunately, I did not record the author or the title of that post. Within the approach of that old post a palette is created to insert all possible pairs of parentheses. Below I reproduce the code from that post:
This works on DisplayFormula cells and satisfies all three requirements. Hope this helps.
Button["Insert Alignment Marker",
Button["Turn on Alignment",
SelectionMove[InputNotebook, All, Cell];