Based on how people normally determine "normal" stocking, 1 inch of fish (fully grown) per gallon, you are about there.
Personally, i over filter, go heavily planted and push the stocking over what would be considered normally stocked into a heavy stocking. I do 50% weekly water changes and my nitrate stays really low. Everything is happy and healthy.
The corys will occupy the bottom of the tank where your existing fish arent, so thats a plus. If you keep on top of your water parameters with water changes i would say 6 or 8 smaller corys would be fine. Pygmy corys will be about the same size as your neons, that would look good. However, i would let your tank settle for a bit, see what your water change schedule is to keep parameters in check before adding anything new in. If your nitrate isnt getting out of control you can add some more fish in.
Your tank doesnt look overcrowded to me.