Correct answer: Implement required changes to the Process API implementation so that, whenever possible, the Process API's RAML definition remains unchanged.
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Key requirement in the question is:
>> Approach that minimizes the impact of this change on API clients
Based on above:
>> Updating the RAML definition would possibly impact the API clients if the changes require any thing mandatory from client side. So, one should try to avoid doing that until really necessary.
>> Implementing the changes as a completely different API and then redirectly the clients with 3xx status code is really upsetting design and heavily impacts the API clients.
>> Organisations and IT cannot simply postpone the changes required until all API consumers acknowledge they are ready to migrate to a new Process API or API version. This is unrealistic and not possible.
The best way to handle the changes always is to implement required changes to the API implementations so that, whenever possible, the API's RAML definition remains unchanged.