With the popularization of transportation network companies (TNCs) (e.g., Uber, Lyft) and the rise of autonomous vehicles (AVs), even major car manufacturers are increasingly considering themselves as autonomous mobility-on-demand (AMoD) providers rather than individual vehicle sellers. However, matching the convenience of owning a vehicle requires providing consistent service quality, taking into account individual expectations. Typically, different classes of users have different service quality (SQ) expectations in terms of responsiveness, reliability, and privacy. Nonetheless, AMoD systems presented in the literature do not enable active control of service quality in the short term, especially in light of unusual demand patterns, sometimes allowing extensive delays and user rejections. This study proposes a method to control the daily operations of an AMoD system that uses the SQ expectations of heterogeneous user classes to dynamically distribute service quality among riders. Additionally, we consider an elastic vehicle supply, that is, privately-owned freelance AVs (FAVs) can be hired on short notice to help providers meeting user service-level expectations. We formalize the problem as the dial-a-ride problem with service quality contracts (DARP-SQC) and propose a multi-objective matheuristic to address real-world requests from Manhattan, New York City. Applying the proposed service-level constraints, we improve user satisfaction (in terms of reached service-level expectations) by 53% on average compared to conventional ridesharing systems, even without hiring additional vehicles. By deploying service-quality-oriented on-demand hiring, our hierarchical optimization approach allows providers to adequately cater to each segment of the customer base without necessarily owning large fleets.