Large language model tutors are easy to build in a notebook and hard to run in a real course. We describe ITAS (Intelligent Teaching Assistant System), a multi-agent tutoring system that a graduate quantum computing course used for a semester at Old Dominion University. The system has three layers. The teaching layer is a Spoke-and-Wheel of three parallel specialist agents (Video, Code, Guidance) followed by a Synthesizer, plus a separate autograder that evaluates both the correctness and the approach of checkpoint submissions. The operational layer is four Cloud Run microservices with session state in Cloud SQL and interaction events streamed through Pub/Sub to BigQuery. The feedback layer is a narrow-scope conversational agent that answers instructor questions over per-lesson pseudonymized event streams, addressing what we call the Blind Instructor Problem: LLM tutors accumulate more data about students than the instructor can reach through routine channels. The architecture is a direct response to specific failures of an earlier prototype, and we describe which of those fixes carried forward and which were dropped for this iteration. We report on a pilot deployment (five students, one course, one semester) interpreted as system-behavior evidence rather than learning-outcome evidence: the teaching layer handled 334 chat turns without the task-boundary hallucinations that domain consolidation would have risked, the operational layer captured 10,628 events across five modules, and the feedback layer surfaced two findings the instructor acted on mid-semester. We do not claim the pilot generalizes. We do claim that the system as described is one workable answer to the question of what an LLM-based ITS needs to look like end-to-end to run in a real course.