It isn't entirely clear, but I think the options on a charge are exclusive. Anyone has an option of making a bull rush instead of their regular attack as part of a charge. A creature with pounce can make a full attack, instead of just an attack action as part of charge. I don't think you can do both though.
Basically, the bull rush and the full attack are both replace the regular charge attack action, so you have to choose which one you want to take.
What Dave Justus said, except your idea would work with the Knockback rage power.