No block rates

What do they offer for setting aside a group of rooms? If they don’t allow block rates or any guarantee that they can be reserved without you paying for them, then expand the radius outward until you can locate a hotel that offers a block.

If they do not offer a rate I would still block the rooms as long as it’s a courtesy block. You at least will guarantee guests that rooms will be available since you mentioned it’s a popular tourist spot.

I would recommend using a (free) service to help you with this. We used Kleinfeld Hotel Blocks (I filled out the forms for that and Hotel Planner, which is another option, but Kleinfeld was more personal so I liked it better). Our contact person there found a bunch of them for us and then handled most of the communication with the hotel we chose, even when we had to reschedule because of covid and also had to make a few more changes later.
We didn't have the issue of hotels around us not offering blocks (as far as I know) when we started the process, but our person definitely knew to contact hotels that I didn't even know existed and she's made/is making the process easier than it would've been for us, so it's probably a decent place to start.