Have you checked into virtual webcam software? You could possibly trick VST Connect by routing its video source from the software’s virtual output.
If I understand rightly, if you’re presenting video to the ‘Performer,’ and you activate Rehearsal mode, the performer will hear you synced with the playback, and the playback will be instantaneous on the Engineer machine, so it seems it would be well suited to that. (Recording in Rehearsal would be out of sync, btw)