The overlay finally works - in fact it did all the time...
The zero coordinates for positioning the overlay are different inside steamVR and DCS. So when I set up the kneeboards position while viewing it in steamVR, DCS elevated it above my head when it started up. And from below it isn't visible as was already pointed out. So for me it seemed to disappear after working nicely outside DCS before. After I set its position up while in-game everything works perfectly well. In steamVR I'm on the floor level now when I start VRK, but I don't bother.
Btw, for me the starting order seems to have no impact on VRK.
Thanks again Panther for your ideas, tips and patience!