We do this for SPA. The POST can be supported just like you explained. Then you can either reload the "page" to see that the checkbox is checked, because backend will include that as part of the page, or (as an optimization) reload just that checkbox if you created a specialized resource for it. The entire page is still there for you to fetch upon transitions.
Among pages, you will still need a few individualized resources sprinkled around for optimizations/reloads/fragment-paginations. The difference between that and a complete API is that they will be entirely design driven. If a table needs paginating, and is built with data from multiple resources, you will not provide 2 resources, and expect front-end to paginate and glue them together. Instead, you provide a complete paginated resource for this table, where data is ready to be displayed as-is.