I think it works to tie it to the month, and it's strange to say the month name when you run it on the 21st.
I'll move it to the 3rd of each month unless it's the weekend, and then I'll push it to that Monday.
The problem is that they get flagged and downweighted because unofficial monthly regular threads are (informally) not allowed here. Otherwise people try to start too many of them, and it's one of those things that only works well within limits.
The solution we hit on with whoishiring (a long time ago) was to make it official, give it basically a system account, and take it out of the realm of individual submissions.