Dear @MOORE, Matthew,
Thank you for posting your question in the Microsoft Q&A forum.
Based on your description, although different engineers are assigned to each service, Microsoft Bookings determines bookable staff on a shared booking page based on overall staff availability rather than isolating staff per individual service.
For a better understanding of your situation, could you please provide a screenshot of your settings so I can support you more effectively? You can go to your Bookings > Services > click on Staff, as shown in my test environment screenshot below.
I have tested this in my environment, and after assigning one person, it showed only one optional person (with private information hidden).
Looking forward to your update.