I've wrestled with this for a while, and it seems like using the Accept header with version in a MIME type parameter (e.g. Accept: application/json; version=1), is perhaps the "right way" to do this. The thing is, forget that and all the headaches that go with it. I want to go with version in the URL.

Much like described in this blog post: https://cloudplatform.googleblog.com/2017/06/versioning-APIs-at-Google.html

The API (not the app) should have a X.Y version where the URL contains /vX. Changes in X are thus breaking (removed or renamed fields, etc.), while changes in Y are not breaking (added fields or endpoints, etc.).