Ended up going a different way. Instead of trying to get the labels/configuration externally, now I'm pushing them from DXA to the consuming applications.
Way to obtain the settings within DXA:
string websiteConfiguration = SiteConfiguration.ContentProvider.
This is a defect. R&D are working on a fix, at this point I'm waiting for confirmation on what timeline I have and will update the note here with the hotfix number.
The only alternative I see at the moment is to iterate through the items returned and make an individual request for each binary item download URL. At up to 1000 a page that's not going to be ...
Not sure if this is helpful, but one way I've retrieved binaries is by first retrieving an "untyped" component (i.e. templateless publishing), and then using the result to find and retrieve any binaries. The second query for binary(ies) should give a URL where the image can be retrieved:
component(namespaceId: 1, ...