Groups that do not have a President and run the way that you are explaining are effectively running with numerous watered down Presidents. By having say four or five "leaders" running the meetings, giving updates, etc., all that is really happening is that there are numerous chiefs. Sometimes the chiefs will stick to their own thing, but sometimes not.
Personally I believe that you have to have the single point person, meaning a President. Actually my group did not have a President for a year and a half before I got involved, but the Treasurer effectively ran things. This is not ideal either as you lose some of the group's checks and balances this way. There needs to be that one person to interact with the Principal on issues that may come up, someone needs to define next year's calandar, someone needs to make up the Agendas and run the meetings. If everyone is focused on their specific function each may get done, and done well, but a PTO has so many things going on at one time that things will just have to fall through the cracks.
My recommendation is to think about who seems to be the person that takes the leadership role most often, and then ask if that person would be willing to do the same thing with the official title. Next, see if all of the other committee leaders would be willing to continue what they were doing with the offical title of Co-Vice President.
Also, with the way your group is presently run, it almost sounds as though the Principal is the President, at least as far as spending. I mean, a PTO should not be thought of as a cash cow for a school's Principal. And though she is not treating you guys this way, things can change, she may move on and you could get a new Principal who may not see things the same way, etc. I would recommend looking at becoming independant. Overall it ends up just being better for the children.
Good luck, PresidentJim