WhatsApp and many other commonly used communication platforms guarantee end-to-end encryption (E2EE), which requires that service providers lack the cryptographic keys to read communications on their own platforms. WhatsApp's privacy-preserving design makes it difficult to study important phenomena like the spread of misinformation or political messaging, as users have a clear expectation and desire for privacy and little incentive to forfeit that privacy in the process of handing over raw data to researchers, journalists, or other parties. We introduce Synopsis, a secure architecture for analyzing messaging trends in consensually-donated E2EE messages using message embeddings. Since the goal of this system is investigative journalism workflows, Synopsis must facilitate both exploratory and targeted analyses -- a challenge for systems using differential privacy (DP), and, for different reasons, a challenge for private computation approaches based on cryptography. To meet these challenges, we combine techniques from the local and central DP models and wrap the system in malicious-secure multi-party computation to ensure the DP query architecture is the only way to access messages, preventing any party from directly viewing stored message embeddings. Evaluations on a dataset of Hindi-language WhatsApp messages (34,024 messages represented as 500-dimensional embeddings) demonstrate the efficiency and accuracy of our approach. Queries on this data run in about 30 seconds, and the accuracy of the fine-grained interface exceeds 94% on benchmark tasks.