I disabled all widgets but every single legacy page (from before I switched to this theme) had widgets on them – the default stuff, ‘recent posts’ etc.
I went through and made sure that I’d removed them all from the sidebar sections, but made no difference. So I literally went through every page and switched out the default template to ‘full width’. That finally did it.
Except now I’m working on the posts (as opposed to pages) and this is showing the widgets on every one. Unlike with pages there are no templates to switch to.