Right. It's the location the software chooses to move it to that will continue to be used for all subsequent conversations, and on PS4 that will not be where you put it, but it is affected by where you put it. I'm hoping SE will eventually fix the placement problem, but in the meantime, you can (at least sort of) work around it.

As the software stands now, don't pull it up to the place where you want it. Pull it up to somewhere significantly farther up than that (and farther up than where you tried before). Then when the software moves it down (on the next conversation), that will hopefully end up where you actually wanted it. (But keep track of roughly where you tried placing it before, so if it still goes down too far, you know to try placing it somewhere higher on your next attempt to drag it up. It takes a bit of trial and error to get it to work.) You have to find a setting so that the location it chooses to move it to is what you want (or close enough, as it seems to have only certain possible places it will pick between).