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If you want your media types to be "evolvable", make that point very clear in the documentation. Similarly, if the placement order of fields is not guaranteed, make that explicitly clear too. If you supply sample code for your API, make sure it does not rely on field ordering.
However, even assuming that you have to maintain different versions of your media types, you don't have to version the URI. REST gives you the ability to maintain the same version-agnostic URI but use HTTP content negotiation (via the Accept and Content-Type headers) to offer different payloads at the same URI.
Accept
Content-Type
Therefore any client that doesn't explicitly wish to accept your new v2/v3/etc encoding won't get it. By default, you can return the old v1 encoding with the original field ordering and all of those brittle client apps will work fine. However, new client developers will know (thanks to your documentation) to indicate via Accept that they are willing and able to see the new fields and they don't care about their order. Best of all, you can (and should) use the same URI throughout. Remember - different payloads like this are just different representations of the same underlying resource, so the URI should be the same.