Here's a thought experiment. Omega offers you tickets for 2 extra lifetimes of life, in exchange for a 1% chance of dying when you buy the ticket. You are forced to just keep buying tickets until you finally die.

This suggests buying tickets takes finite time per ticket, and that the offer is perpetually open. It seems like you could get a solid win out of this by living your life, buying one ticket every time you start running out of life. You keep as much of your probability mass alive as possible for as long as possible, and your probability of being alive at any given time after the end of the first "lifetime" is greater than it would've been if you hadn't bought tickets. Yeah, Omega has to follow you around while you go about your business, but that's no more obnoxious than saying you have to stand next to Omega wasting decades on mashing the ticket-buying button.