I think it's a bit confusing that you have to click the timestamp to get the direct URL. I suggest clicking on the message itself. (And yes, that means remove the pop-up feature.)
Changing the URL like Twitter does would help, but to me it seems better to load a new page. Keep the pages simple so that they load fast. You are doing an excellent job at this.
I support this idea. Don't mind the pop-up too much but it should maybe include context if it's a reply like Twitter does and show a little more of the thread/convo?