I see some use these kind of titles, but i reckon better alternative is to have Best casinos for May somewhere on the page instead of touching the main title every month.
Google picks it up very well, and it doesn't have to be H2 or H3.
Simply put a bolded note above your casino list and it will do the job.
And the page title can be, for example, Best Online Casinos Australia: Top Casino Sites AU [2021], and you will certainly rank for May and June and other following months too, because you have [2021] in the title and you make on-page notification update for each month every time it starts.
Once someone looks for "best online casinos Australia May" or "Best online casinos May Australia" etc, Google will pull that piece of text from your page and show it instead of your page description.
P.S There is no guarantee that it will work for everyone!