How do I keep the Amazon Connect External Voice Transfer leg off the public internet?

Your assumption is correct. AWS has published a whitepaper titled "AWS Direct Connect for Amazon Chime SDK Voice Connector" that confirms this.

Public VIF is the correct choice

The Voice Connector is a public-facing service and does not reside within a VPC. Private VIFs (for VPC access) and Transit VIFs (for Transit Gateway) cannot be used; instead, a Public VIF is the designated method for connecting to public services like S3 and the Voice Connector.

Destination must be a public address

The "termination allowed IP list" for the Voice Connector accepts ranges between /32 and /27, and these must be public IP ranges. RFC1918 addresses are not permitted.

However, "having a public address" and "traffic traversing the public internet" are separate issues. If you advertise your registered public prefix over the Public VIF, the addressing remains public while the traffic path stays within the Direct Connect connection. This is precisely the configuration you envisioned.

Key steps

1. Create a Public VIF and establish a BGP session.
2. Advertise your registered public prefix.
3. Add the SBC's public IP to the "termination allowed IP list."
4. Verify that the return path from AWS to the SBC routes over Direct Connect using that prefix.

Since Direct Connect itself does not provide encryption, using SIP TLS and media SRTP (supported by the Voice Connector) alongside it ensures both traffic isolation and encryption.

Whitepaper: https://d1.awsstatic.com/Products/product-name/Chime/AWSDirectConnectforAmazonChimeSDKVoiceConnector.pdf

One point worth verifying is whether you can manually control the "termination allowed IP list" for the Voice Connector used internally by Amazon Connect's external voice transfer connector. To be certain about the extent of configuration exposed within the managed Amazon Connect setup, you should check the actual environment or consult AWS Support.