In fact, the <forward_cookies> setting should have allowed you to receive the cookies in NotifyUser.
To check if the request is received by the Server in the same form it is sent by the client, you can have it logged by setting the LightstreamerLogger.connections.http logger at DEBUG level.
Moreover, you can check if the request is forwarded correctly to the Remote Metadata Adapter by setting the LightstreamerProxyAdapters logger at DEBUG level.
Both log settings are verbose, so they are most useful if you can replicate the issue in a test environment.

But note that the <forward_cookies> setting should be in the main configuration file, to act on a global level, not in adapters.xml as you report.
Please clarify that first.