This sounds really interesting and like good engineering (tm), would you mind sharing which company this was for? Maintaining good blackbox e2e tests and the infrastructure is one thing, finding time (and space in the roadmap) to do that and load test on top of that is a great engineering indicator IMO.
I wonder if it would be possible to translate regular recorded user activity (assuming the API was instrumented) for it and find some way to randomize & generate it (a la quickcheck) and re-feed it into the system. There are some sticky points like pre-existing state (if you take the recording of any given day), but you could probably discover/evaluate that from API requirements (if you saw a `GET /resources/1` which succeeded, then obviously a `POST /resources` must have occurred before hand).