Testing http rest APIs that have long running queries that are polled for status

I'm struggling to find a framework to help me test the performance of a service I am writing, that has a long running process it fronts. A simplified description of the service is:

1. POST data to the service /start endpoint, it returns a token.
2. GET the status of the action at /status/{token}, poll this until it returns a status of completed.
3. GET the results from /result/{token}.

I've dabbled with Locust.io, which is fine for measuring the responsiveness of the API, but does little for measuring the overall end to end performance. What I would really like to do is measure how long all three steps take to complete, particularly when I run many in parallel etc. I should imagine my service back end falls over far sooner than the rest API does.

Can anyone recommend any tools / libraries / frameworks I can use to measure this please? I would like to integrate it with my build pipeline so I can measure performance as code is changed.

Many thanks