Non nude beach
I'd found a spot with sawgrass that made a great place to have some privacy. Once when I was laying there, a woman poked her head over the weeds, and we greeted each other. I asked her if she would be ok if I stripped down. She said it wouldn't bother her, and she said would even warn me if any kids were coming our way! Sometimes it's better to ask than to be surprised by an officer.
I've even been at another beach to watch the sunrise. I was a bit early and it was still dark when I got there. No one sitting anywhere near, but a lot of walkers. Being it was dark, I decided to strip down until after the sunrise. Some sat down fairly close, so I asked if it were ok as I was. They were like, whatever.
I've never tried that approach, but rather tried to pick spot quiet enough to be undisturbed. Could be an approach in the right circumstances, though.
As you write, picking a good spot is important, but sometimes there are others around which cannot be avoided. If they look to be amenable to a little nudity I will ask. Sometimes they are there for the same reason but are not sure about getting naked until someone breaks the ice.