How can I troubleshoot extremely slow responses from Google Play Android Developer API occurring only on production servers?

We have been using the Google Play Android Developer API to verify subscriptions on the backend for several years without major issues. A few days ago, we noticed that calls to verify subscriptions were becoming extremely slow (with calls succeeding, but lasting a minute or longer), and this is disrupting our validation flow with the app.

No errors result from the Google Play API call, it is only taking a long time to return. The issue reproduces consistently, on our production servers, when querying for subscriptions on a specific Google Play app. The issue does not reproduce when running on our test servers or on another Google Play app, despite using the same credentials and Google Play API endpoint. According to the Google Cloud Console, we are far below the quota for API requests.

The Google Cloud status page reports no incidents. We have opened a "support" request on Google Play, with no response as of 3 business days later. Has someone else experienced this problem? (Is there a contact, forum, or issue tracker for this kind of service disruption?)

Source: Android Questions