Is there a way to make skill points? Instead of using Gold or Job Points as currency, is it possible to receive SP after a battle that can be used to unlock skills in the skill tree?

You could use jobpoints and limit the once you get to just level ups.
You could also use an item that cannot be sold that represent skillpoints. Be sure to create one for each character.

Create an invisiable item and use the ID as a cost and call it a skill point