ok, I've worked it out, so you don't use the cid directly, you need the model id instead (you can get that from the cognitive services speech studio when you create the model)
then you hit the CreateTranscription endpoint and include:
"model": { "self": "https://northeurope.api.cognitive.microsoft.com/speechtotext/v3.0/models/{model id}"}
in the data you post.
you can check in the response when you submit that the right model is used, if you make a mistake (e.g. leaving out the 'self') then it will just use the default model.