Hello pleechford,
There are a lot of really great species that do very well in a 10g planted tank.
Unfortunately, skirt tetras and emerald corys are not among them. Both of those fish should really be housed in 20g minimum IMO. They are schooling fish and should be kept in a school to avoid stress and to see their full spectrum of behaviors.
I am also going to add that IMO, cardinals do not belong in 10g.
Here is a brief list of some nano fish that do well in a tank that size with plants: ember tetras, chili rasbora, microrasbora, sparkling gouramis, croaking gourami, betta, dwarf gourami, pygmy corys (pymgaeus, habrosus, hastotus), scarlet badis, guppies, platys, Asian stone catfish, black phantom tetra, and neons or green neons (these are not the same species).
Since you already have a few neons, I would suggest you re-home the emerald cory and the bst, get 3 more neons, and one of the suggested gouramis or else a couple of male guppies or a couple of platys.
Also, nerite snails!