At my high school, the original role of the
TD was to be in charge of anything tech-related, including scheduling, choosing of crew heads, design,
etc.
It's been quite redefined at our sudden lack of a TD in the formal sense, since our previous quit due to various reasons, one of which was his moving. We don't much see out TD anymore, besides on paper and for general supervision in the shop. However, our tech department has taken a hit due to this, so even if it becomes overwhelming at first, I hope you're able to keep track of all of your crews so that doesn't happen at your school as well. Granted, I'm sure you're a much better TD than our previous, so...
I'm impressed that you manage
house as well. It's unfortunate that you much eliminate some staff, but perhaps - if your house system would make it possible - teach a student or two how to run house? It's been working well at my school for awhile, but again, I don't know how your house is run so it may not work.