LOL! You have to use the privacy screen in conjunction with your tray table! That's why the releases for both tray tables are located right in the middle divider between the twin seats. Just release the tray table by pressing the respective button, but don't unfold the tray. The released tray, in conjunction with the smaller screen you already mentioned, provides for perfect privacy when your seat is in bed mode. And no, this isn't me improvising, the thing was actually constructed to work this way. Funny that you didn't realize the magic behind that piece of German engineering.

Oh, and yes, it pays off to be a nice guy. 90% of my flying is with LH, on longhauls always in C or F (mostly upgrades), so I know the product very well and have a good idea of LH's variance regarding service quality and consistency. By being nice and connecting to the staff (and please never confuse being nice with sucking up, which usually doesn't leave a good impression), I have received several op-ups and, on many occasions, superior treatment. Of course, YMMV, and there have also been a few bad episodes with LH staff. Luckily, being nice doesn't mean one has to be weak. When somebody treats me badly or trys to take away my rights despite me being nice, I'm very much able to change gears and get what I'm entitled to. But of course it's so much better to achieve this goal while EVERYBODY's feeling good about it.