713990 All other amusement and recreation industries
512290 Other sound recording industries
541690 All other scientific and consulting services
SIC Code are better; https://www.naics.com/sic-industry-description/?code=7922
I've been using "711512 - Independent actors, comedians and performers" for freelance work, but it looks like that's a Canadian-specific code. The US has a similar code ("711510 - Independent Artists, Writers, and Performers") which should cover US freelancers in our industry.
For a larger operations, there's some suggestion online that the Broadway sound provider Sound Associates was using "711320 - Promoters of Performing Arts, Sports, and Similar Events without Facilities", which is less of a stretch than it sounds after reading the examples given, whereas it looks like Eighth Day (and some others) may have gone with "532490 - Other Commercial and Industrial Machinery and Equipment Rental and Leasing".
Lots to choose from!
-Russ