The third path: fine-grained object-capabilities and attenuation based on data provenance. More simply, the legs narrow based on what the agent has done (e.g., read of sensitive data or untrusted data)
Example: agent reads an email from alice@external.com. After that, it can only send replies to the thread (alice). It still has external communication, but scope is constrained to ensure it doesn't leak sensitive information.
The basic idea is applying systems security principles (object-capabilities and IFC) to agents. There's a lot more to it -- and it doesn't solve every problem -- but it gets us a lot closer.
Happy to share more details if you're interested.