I actually replied without actually responding to your post here by accident, didn't even see your post until now here but over on that other forum we use I
talked about ground planes for Inverted L's.
There's a claim that placing an equally length wire along the ground as the horizontal; aired part of the vertical section is beneficial. I'm not sure if that's fact though, might take some computer analyses. That horizontal section is not really radiating much anyway so I feel the most important part of that section acts as a loading coil for the vertical section or capacitance hat, and by placing a length of ground plane along the same direction will simply add to aerial capacitance thus probably plays with overall loading efficiency.
Now as far as directional qualities of the L, the long part horizontally longitudinal is the direction with a possible loss of 1dB. Put the length of the inv. L behind the area you want to give the strongest signal, but 1dB is so little it probably will have little effect anyway.
I've also noticed that sloping L's exhibit some interesting features. If you slope the inv. L the sloped section seems to have a far lower angle of radiation, thus if you are on the outskirts of town like me and want to hit your town strongest with frontal ERP, you put the sloping section toward your town and the ground screen same direction.
I may be wrong on some of this, but these are my observations in reality when testing.