Conference recordings when all calls from outside system

I’m wondering how users can retrieve call monitor recordings from conference calls where all participants are dialing in from outside numbers? The conference might be one that is set up to record all calls.

Normally the uniqueid or match based on the callerid/extension is used to find matches in the ARI user portal. The matching algorithm won’t work when the callers are all external.

Does anyone know how this would be handled using the standard conference module in lieu of Web-Meetme?