In crowdsourcing systems, requesters publish tasks, and interested workers provide answers to get rewards. Worker anonymity motivates participation since it protects their privacy. Anonymity with unlinkability is an enhanced version of anonymity because it makes it impossible to "link" workers across the tasks they participate in. Another core feature of crowdsourcing systems is worker quality which expresses a worker's trustworthiness and quantifies their historical performance. In this work, we present AVeCQ, the first crowdsourcing system that reconciles these properties, achieving enhanced anonymity and verifiable worker quality updates. AVeCQ relies on a suite of cryptographic tools, such as zero-knowledge proofs, to (i) guarantee workers' privacy, (ii) prove the correctness of worker quality scores and task answers, and (iii) commensurate payments. AVeCQ is developed modularly, where requesters and workers communicate over a platform that supports pseudonymity, information logging, and payments. To compare AVeCQ with the state-ofthe-art, we prototype it over Ethereum. AVeCQ outperforms the state-of-the-art in three popular crowdsourcing tasks (image annotation, average review, and Gallup polls). E.g., for an Average Review task with 5 choices and 128 workers AVeCQ is 40% faster (including computing and verifying necessary proofs, and blockchain transaction processing overheads) with the task's requester consuming 87% fewer gas.