I don't know if this solves very much. As you say, if we use the number 1, then we shouldn't wear seatbelts, get fire insurance, or eat healthy to avoid getting cancer, since all of those can be classified as Pascal's Muggings. But if we start going for less than one, then we're just defining away Pascal's Mugging by fiat, saying "this is the level at which I am willing to stop worrying about this".

Also, as some people elsewhere in the comments have pointed out, this makes probability non-additive in an awkward sort of way. Suppose that if you eat unhealthy, you increase your risk of one million different diseases by plus one-in-a-million chance of getting each. Suppose also that eating healthy is a mildly unpleasant sacrifice, but getting a disease is much worse. If we calculate this out disease-by-disease, each disease is a Pascal's Mugging and we should choose to eat unhealthy. But if we calculate this out in the broad category of "getting some disease or other", then our chances are quite high and we should eat healthy. But it's very strange that our ontology/categorization scheme should affect our decision-making. This becomes much more dangerous when we start talking about AIs.

Also, does this create weird nonlinear thresholds? For example, suppose that you live on average 80 years. If some event which causes you near-infinite disutility happens every 80.01 years, you should ignore it; if it happens every 79.99 years, then preventing it becomes the entire focus of your existence. But it seems nonsensical for your behavior to change so drastically based on whether an event is every 79.99 years or every 80.01 years.

Also, a world where people follow this plan is a world where I make a killing on the Inverse Lottery (rules: 10,000 people take tickets; each ticket holder gets paid $1, except a randomly chosen "winner" who must pay $20,000)