I came up with a related strategy that avoids estimating times. Take turns starting from the dealer’s left. If you can play the next card in sequence, do, otherwise pass. The player on your left will eventually realise you’re passing. If the pass goes all the way round the table, that card isn’t in anyone’s hand, so you test in the same way to see if anyone has the next card.
Of course, this also trivialises the game, so it wouldn’t be used.