Has he defined teacher approval? Do you have a teachers rep?
Maybe the best thing to do here is nothing! I know that will be hard to do, but, you need the support of the teachers and the parents, the best way to obtain this as you have described the problem is to make them aware of what they lose without a PTO.
Another thing I might suggest is to find out what this new principal's goals are for the year and find things that will support him on this. This is a value add to him.
My new Principal was weary of how my new board would or would not benefit her. Early on we began things that would back her on achieving these! This is a reality that all PTO/PTAs have to realize and understand. Yes it is political, I know you arent there for the polictics! But if you buck the politics your organization will lose everytime!
Here is an idea, you have honor roll assemblies? See if you can't get your state representative )or other such high muckity muck) to give a short address at it! If they will agree pending the approval of the principal, go talk to the principal about it!
We have a new principal that won't make any decisions at all. He doesn't want to be involved and spilts as early as he can. Our last principal was a total control freak and wouldn't let anyone else handle or decide anything. As a result, the teachers aren't used to taking the lead in anything and now that decisions are being passed on to them exclusively, things aren't going well. We've always had a strong PTO but we can't do much if he won't let us proceed without teacher approval. Any advice?