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.
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.
The solution in normally to rest the screen against the seat in front.