This is why I harp on this forum about everyone needing an umbrella policy on top of their liability policy for their Cobra. Your next treat could be a "day in the life film of Lisa M."
If we wind up in court, either at the defendant's table or for a simple traffic ticket, the fact that we were driving a Cobra is one and half strikes against us from the get-go. In my neck of the woods, anything under a couple million is prima facie underinsured.