Well, if we end up going with this style, here's my badge:
EDIT: Templates illustrating the shading style:
The edge outline colour has to be the same across all badges, since the small versions will be sharing edges when arranged as above. The upper-left and lower-left edges of the badge have highlights and shadows to give it depth.
Otherwise, each badge should use white for the main design, outlined in the darker shade of the main colour. The lighter shade can be used to smooth edges inside the white area. On the lower-right edge of the badge, white is replaced by the light badge colour, while on the top-left, the dark colour is replaced by the base colour. The different shades can be used for smoothing (as on the Ground-type example badge).
Looks pretty good. I'm ok with this type of badge.