I made some attempts on something pretty similar some years ago, but put the editing interface into a bubble. At the same time the pencil icons were added to the infoboxes, they linked to the property hash mark, and having two interfaces created confusion. Pretty soon it became pretty obvious that the pencil solution had some serious issues when a row in the infobox used two or more statement and especially when those two statements used different properties.
I tried out a couple of access methods. One added a tool link to the left of the row on hover. That worked quite well, but failed on being clear on the confusing two-statement problem. An example of the problem is a single infobox row with both a birth data and a birth place. I made a popup menu on the row itself, having two entries, but even when that worked the two-level menu-like behavior was somewhat cumbersome.
The solution is quite obvious. Editing a row that uses two statements are really about editing two statements (That is a bomb-shell!) and only editing one is enforcing the wrong process. Click on the row and open both statements in one and the same bubble.
The way identified the properties for editing was by adding them as classes, but a better way is probably to use data attributes.