Urban air mobility (UAM) refers to air transportation services in and over an urban area and has the potential to revolutionize mobility solutions. However, due to the projected scale of operations, current air traffic management (ATM) techniques are not viable. Autonomous systems leveraging AI techniques are a pathway to accelerate the realization of UAM operations, but must be fielded safely and efficiently. The heavily regulated, safety critical nature of aviation may lead to multiple, competing safety constraints. In this paper, we design a framework which allows for the scalable planning of a UAM ATM system. We formalize safety oriented constraints derived from FAA regulations by encoding them as temporal logic formulae. We then propose a method for autonomous UAM ATM that is both scalable and minimally violates the temporal logic constraints. Numerical results show that the runtime for our proposed algorithm is suitable for very large problems and is backed by theoretical guarantees of correctness with respect to given temporal logic constraints.