I have a unique position in that I teach drama at Baptist high school and am required to attend multiple services during the week. Of course, we don't even think about rehearsing on Sundays or Wednesday nights (the mid-week) service. For 3 of the 6 services during the week, I am the audio technician, and I occasionally fill in for the other services.
When I work in theatre outside of the high school, I have learned to schedule soundboard replacements for my duties during tech weeks. It's part of life in the theatre--a compromise between church and theatre that I have had to come to terms with.
Many Baptists would criticize me for putting theatre before God and church. This is a topic for another thread, but I do wonder if your SD is struggling with this issue himself.
As for just going to another church with an earlier or later service, it doesn't work that way in the Baptist religion. Just like there are Missouri Synod Lutherans and Evangelical Lutherans, the Baptist has many branches: American Baptist, Southern Baptist, and Independent. Each branch has variations in doctrine, and the independents can vary from charismatic to fundamental. In most areas you won't be able to find more than one church that preaches the same way you believe.
Since the original post is about a college production, I wonder if the SD just has not run into this issue before--having tech's rescheduled in the middle of a church service. The experienced SM will plan for it, but other technical and artistic crew members may not think that far ahead. I hope that he will think about this experience before taking another position.