Thanks so much for this solution @Nicklppolito It works brilliantly, I've been in contact with Squarespace and Vimeo all day to find a way to get this working! I had them embedded using the standard autoplay embed, added recommended parameters, but only some would autoplay at random every refresh. Or sometimes, not at all.
This method sorted it. I notice on Mobile the player's Profile, title and share icons are always visible. Controls seem to hover in/out. Any ideas if we can remove those? No worries if not, just happy to have it consistently autoplaying at this stage!