So if you wait for the cooldown time and use the skill again, you don't heal at all?

Can you use the dragon morph stone in the first dragon battle, to transform back to human to heal? I think that may be blocked.

Try removing the head piece, and see if using level 1 of Dragon Spirit works any better (it should heal 50 points per second, for 5 seconds).

You can use potions in dragon form, and once you return to the battle tower and upgrade the runners, ingredients are easy to get. Try any food / healing / rejuvenation potions you have.