So what did you do? Clearly you didn't die. Did you just have no insurance for the week before the new job started, or what?
This also happened to you while you were working and slightly between jobs. So it's not really a FIRE concern if the concern is the US messing up the health care system even more in that it would effect everyone whether working or not. Generally speaking, an answer to mitigating a lot of types of risk with a FIRE model is: you just go back to work for a while. This is easier the younger you are.
Edit: Also I thought COBRA would have been a more recent thing but it was Regan era. So did you not have employer-sponsored coverage with the startup?