Thank you! I kept that in mind and checked the points calendar every few hours: at first, the calendar was empty of availability, but then a couple of nights in June would show up individually (seemingly at random) and I would book them. After 5 days of checking the calendar a few times a day, I had been able to 10 nights in total for an average of 50k points each. I reached out to my Ambassador to have the nights merged into a single stay and they explained that it's not possible to merge points stays, however, my Ambassador spoke to the hotel and they will treat it as a single booking with a single room for the duration of the stay -- which was the intended outcome, so, all good.

For anyone else who might have the same question in future, my full process was...

1. Go to the Marriott website
2. Search for 1 night flexible in your target month
3. Bookmark the resulting page
4. Check the page a few times per day, booking stays each time one of your target dates becomes available
5. After all nights are booked, contact your Ambassador (or the hotel directly) to ask for the nights to be treated as a single stay

At the time of writing, only the 29th of June is available for points (52k) but over the last week, every other date in June has been available, so it just requires patience! I didn't notice a pattern in when dates became available, it seems to be random, or perhaps it's based on when other guests cancel.