The antonyms for the phrase "banged heads" could be anything that implies harmony, cooperation, or agreement. Words like "collaborating," "cooperating," "concurring," or "conspiring" all suggest a positive and unified approach to a problem rather than the head-to-head friction of two opposing forces clashing. A phrase like "brainstorming together" might convey the sense of a group working together to find a solution, rather than two individuals locked in heated debate. Whatever the antonym, it would need to convey a sense of mutual respect and harmony, rather than a combative or divisive approach.