The fucked up (statistical) lives of Alaskans are more reasonably attributed to the lack of women. First, note that on many measures of health and wellness, men do worse than women, so the average Alaskan will do worse on these even if there's no true gender-controlled difference.
On top of this, consider the effects of few women on a heavily male population. Depression, binge drinking and violence are not terribly surprising.
Separately from the relative lack of women itself, consider one of the reasons there are fewer women: dangerous, unpleasant seasonal employment in large portions of the economy. This will first tend to bias the population toward people who are willing to work in such jobs, and second there will be an effect of such occupation on them.
It's also important to note that almost all of the population is concentrated in southern cities that have sunlight every day of the year.
Sunlight might be a possible factor, but it should definitely be below any of these on your list unless you have very strong reasons to believe otherwise.
