If the server generates custom mimetypes, clients have to ensure they "Accept:" the correct mimetype for every request.

No, he doesn't. First, the server can send whatever it wants - nothing breaks if you reply with your custom media type to a generic "application/json" request.

Second, even if you want to be correct, that's what wildcards are for: the client can simply send always the same header:

     Accept: application/*+json

If the server generates custom mimetypes, and you update your API to v2 which produces an article listing in an incompatible format, you either have to introduce a version number into your mimetype (which seems messy and pointless busywork),

I still don't get what's the problem with changing a string. I think you're using a bad framework.