Things like this are why mTLS internally are so important. If a hole is found in your firewall, services still don't trust each other until they have a valid TLS certificate.
If you're exclusively interested in mitigating SSRF, a more targeted solution is to run your connections (HTTP or TCP) through a proxy that enforces network-level rules. That seems like it would have worked here. For HTTP SSRF, Stripe has a good tool, Smokescreen.