We actually had the topic only recently
You want to purge the cache Cloudflare-wide, not just in the datacentre where the Worker is running, correct? In that case the API is the right approach.
Purging can take a couple of seconds, but it shouldnt take ten minutes. Did you check all caching relevant headers? Are you absolutely sure the file didnt get cached and maybe re-added?
If you are sure, open a support ticket and let them know the result.id of that particular purge request. They might be able to tell you more.