An illustrative multi-access server orchestration system determines a subset of a set of multi-access servers associated with a communication network. The subset corresponds to a service area of a network anchor point through which network traffic on the communication network is routed to a client device. The multi-access server orchestration system orders the multi-access servers included within the subset to form an ordered listing of multi-access servers from a most-preferred to a least-preferred multi-access server for fulfilling a service request for the client device. The ordered listing designates a first multi-access server included in the subset and located more proximate to the network anchor point than to the client device to be more highly preferred for fulfilling the service request than a second multi-access server included in the subset and located more proximate to the client device than to the network anchor point. Corresponding methods and systems are also disclosed.