I appreciate the advice - unfortunately no luck. I tried the sandbox again just now:

I'm getting a 404 error on the Subscription API endpoint - I think it's because that end point is not enabled (?) if that dashboard OrgID doesn't have subscription licensing:

They don't show the licensing screen in the DevNet Sandbox (that I can see but would love to be wrong here) so I don't know which licensing model is in use but I think it's co-term (just based on the vintage of the Sandbox).
So, my guess is that there is no test environment that has subscription licensing and so that there are no subscription API end points available to test against. I think that's why my test calls are all coming up 404 but obviously a lot of guesswork here.
All the same, I do appreciate your help! I might need to go find a friendly production environment I can test against.