I think you're sort of on the right track about values being root goals. Values come first, then we execute policy based on those values. One goal may come at the expense of another. And some lefties might not even recognize a trade off if statistically they don't value something that conservatives value very highly. Or vice versa.
Your last point is in alignment with everything I've said before. We have the same over arching goal (happiness), we just disagree about how to get there. The two paths to the goal are mutually incompatible, not the goal itself. The path is what is in question and conflict, not the goal. This is why it is so important that the path is discussed honestly and openly. Good intentions do not automatically lead to good outcomes, and if we as a society choose the wrong path we are f*. So to bring it full circle, this is EXACTLY why we need more conservatives on campus: to discuss the other paths and evaluate them objectively so that the best path may win.