Hello my friend!
I understand what you need, and it seems to me that there is no way to do this through the use of connectors.
Unfortunately, Niall himself communicated this in a 2021 post, but they are working to find a way to improve this. (Post in below!)
This happens because when the connector does not get any response from the server, it soon creates an incident, and thus it is not possible to do anything else in camunda except the retry manually.
So in this task I suggest you use JavaDelegate instead of http-connector, because in a delegate you can do the treatment even before generating the incident using a try / catch involving the REST call, and in case you are unable to make the call, throw Bpmn Error…
Hope this helps.
William Robert Alves