I came up with ...Nxe3, taking enough time to do so that an opponent might have wondered what was taking so long. (Though they certainly would have known better than to ask while the clock was running in a tournament game.)
Mr. Fritz concurs: ...Nxe3 with mate in 3 is superior to ...Rg6 with mate in 4 since mating more quickly reduces the chances that an unexpected burst brain aneurysm will force forfeiture due to death.