You can interleave encrypted and unencrypted segments without DISCONTINUITY tags (assuming there is continuity otherwise) by using EXT-X-KEY to specify the encryption (or not) of the init / media segments. A brief audio dropout across the transition is a known issue. Please file an enhancement request if that creates a problem for your application.

Please file a feedback ticket to guarantee that the WebVTT engineers see your report.

The most common reason for the player to stop specifying the _HLS_part parameter is that it detected non-compliant LL-HLS spec behavior from the server and fell out of low-latency mode. You can check if that happened by looking at the AVPlayerItem errorLog.