It would be nice if double clicking a word displayed information about the word by default, with the other double clicking options (search, note, share) displayed as buttons underneath the information popup.
Basically, the way Kindle does it?
I'm on iOS but I think Logos tries to keep the mobile platforms similar. Your suggestion would solve another problem; on a small screen (iPod) you always have to scroll the menu sideways to highlight. Even with a stylus, it takes good aim.
An info popup with stacked menu items would solve several headaches.