That's still a window that's not right next to the completion menu. If I wanted to use a separate window far away from the menu, I'd use the 'preview' window that was designed for this (and YCM does use it, because there's nothing else on the table).
Have you checked the "balloon help" functionality? This was intended for use with mouse and windows for things like tooltips, but I think it may be general enough to expand for use you're looking for. My memory isn't so great but I fooled around with it a couple years ago; if you haven't checked it out you may want to. See ':h balloon'
I just looked back into use of the Vim 'balloon' feature. I think the ballooneval and balloonexpr would do the job fine, the only fly in the ointment is that the help window is tied to the mouse cursor position in two ways. First, the window can be triggered to appear only if the mouse cursor is on a character in the Vim window, not if it's in blank area (e.g., to right of text) or not in the Vim window at all. Second, the help window is always positioned with upper left corner at mouse cursor position. I don't think Vimscript offers any way to position the mouse cursor programmatically, which is what it would take to make Vim's balloons work for desired sort of help display. Perhaps Python could be used to position the mouse; might not be so bad given that Python is required for YCM already. Would require being able to map Vim text cursor position to global desktop xy grid (':winpos' might help) and move mouse cursor to it. . . (Or alternatively hack the Vim source to allow alternative coordinates (e.g., text cursor position) for display of balloon window.)