Most of the domestic airlines in Australia gave fairly shallow tables that aren't deep enough for the stand if you're in cattle class.Wow, that's some seriously small plane/tray. I don't think I've every seen an airline tray that's less than 6" deep front to back (1/2 of overhang f/b of the typecover). When I go into "tent" mode, I flip the keyboard around so that the outside of the cover is resting on the table/tray surface. The flocking/suede on the outside of the cover makes for a pretty good non-sliding interface on smooth tables.
The solution in normally to rest the screen against the seat in front.