There may be some redundancy in my answers because I’m just answering as I go along. Sorry for that.
This works fine with shadows disabled, however, when shadow casting is enabled, the trees cast shadows onto themselves and the 2d cards I use for the fronds/leaves become very obvious:
I’ve never tried it with static lighting, but if you’re using a masked material for your setup for the imposter sprites I wouldn’t think it should matter here. You may need to check the option for Cast as masked shadow in the material settings though. In Kite Demo where we only used Dynamic lighting the PixelDepthOffset_Foliage node or use the VolumeShadowMap material function as a way to adjust the shadowing. It may be best to set this particular material not to cast shadows in the Static Mesh Editor under that Material Element since it can be faked in the material for casting on the actor.
For billboards you shouldn’t worry as much about completely accurate shadow casting for these because usually at that distance the player won’t be able to make out ever fine detail. If the tree mesh itself, and not the billboard, is casting a static shadow that will still be on the ground.
With a Stationary directional light baked shadows are super sharp and a bit messy, and with a static directional light they are softer but the overall problem still remains.
With your stationary Directional Light make sure that you’ve set a Dynamic Shadow Distance for the shadows. By default it is set to 0. At farther distances these will fade out anyhow and shift to the static shadow, so this shouldn’t be a concern for the billboards if they are being used with a static mesh as the higher LODs.