"I had a spring break out of a c melody I'm repadding, but the problem is that the bit left behind in the post won't come out. I've tried gripping it and trying to pull it out and I've tried using spring removing pliers."
Pulling rarely works.
How well spring removal pliers work depends on how carefully the tip is centred on the stump, how flat the end of the stump is, and the type of pliers.
I have found these are sometimes successful where other pliers fail, partly because of the parallel action, and partly because they operate deep into the post:
Scroll to 1187B Spring Install/Remove Plier.
They're not cheap, and sold only to technicians.
"Is is safe to try and tap it out or will this damage the post or body at all?"
1. You must have a firm 'dolly', such as a heavy lump of lead or steel, on the other side of the post. (Lead allows the spring to still support the post while the end of the spring is banged into the lead.)
2. You have little control over what a punch does DURING the impact. It is highly likely to slip off the stump of spring, and embed itself in the softer neighbouring brass, making the spring tighter.