Could Beatty have moved ahead of Jellicoe and crossed behind the German line to impede Scheer's escape?
Short answerPotentially; the maneuver might have blocked the route or forced Scheer to focus in another direction, though the outcome is not certain.
NotesThe proposal keeps Beatty's battlecruisers out of Jellicoe's battle line and sends them ahead with the Third Battlecruiser Squadron. The proposed result is plausible but uncertain. Their position beyond German effective gun range might have closed an escape route or at least forced Scheer to reorient his fleet.