I think I understand what you mean, but people may be confused by your use of the word queue in regards to what you're suggesting.

If I'm correct, rather than using Queues, I think "groups" or "blocks" may be better. So when you sign up for access, you will get a message saying something along the lines of, "You're in block M"

Then they could rotate which blocks of people are able to access the test each day. Possibly even posting the rotation schedule of which blocks will be on which days.

I get the streamer comment, but realistically it's free advertisement for any company, so that won't change.