If you actually have a business case for defense in depth (hint: nobody does - data breaches aren't actually an issue besides temporarily pissing off some nerds, as Equifax' and various companies stock prices demonstrate), what you'd do is have a proxy service who is entrusted with those keys and can do the operations on behalf of downstream services. It can be as simple as an HTTP proxy that just slaps the "Authorization" header on the requests (and ideally whitelists the URL so someone can't point it to https://httpbin.org/get and get the secret token echoed back).

This would make it so that even a compromised downstream service wouldn't actually be able to exfiltrate the authentication token, and all its misdeeds would be logged by the proxy service, making post-incident remediation easier (and being able to definitely prove whether anything bad has actually happened).