I've faced this problem and partially overcome it. I'll try my best to describe this. However, I've also been diagnosed with depression and prescribed SSRIs in the past, so my approaches to handling the problem may not fit you.

You have acquired your estimates of the dangers of the future by explicit reasoning. The default estimates that your emotional, unconscious brain provided you with were too optimistic. This is the case for almost everyone.

Consider that even though you have realized the future is bleak, your emotional, unconscious, everyday-handling mind still hasn't updated its estimates. It is still too optimistic. It just needs to be allowed to express this optimism.

Right now, you probably believe that your emotional outlook must be rational, and must correspond to your conscious estimates of the future. You are forcing your emotions to match the future you foresee, and so you feel afraid.

I suggest that you allow your emotions to become disconnected from your conscious long-term predictions. Stop trying to force yourself to be unhappy because you predict bad things. Say to yourself: I choose to be happy and unafraid no matter what I predict!

Emotions are not a a tool like rational thought, which you have to use in a way that corresponds to the real world. You can use them in any way you like. It's rational to feel happy about a bleak future, because feeling happy is a good thing and there is no point in feeling unhappy!

Being happy or not, afraid or not, does not have to be determined by your conscious outlook. The only things that force your mind to be unhappy are immediate problems: pain, hunger, loneliness; and the immediate expectation of these. If you accept that your goal is to be happy and unafraid as a fact independent of the future you foresee, you can find various techniques to achieve this. Unfortunately they tend to vary for different people.

Expecting to die of cancer in fifty years does not, in itself, cause negative emotions like fear. Imagining the death in your mind, and dwelling on it, does cause fear. In the first place, avoid thinking about any future problem that you are not doing anything about. Use the defensive mechanism of not acknowledging unsolved problems.

This does not mean that on the conscious level you'll ignore problems. It is possible to decouple the two things, with practice. You can take long-term strategic actions (donate to SIAI, research immortality) without acutely fearing the result of failure by not imagining that result.

We are used to think of compartmentalization as an irrational bias, but it's possible to compartmentalize your strategic actions - which try to improve the future - and meanwhile be happy just as if the future was going to be fine by default.

In a similar vein, I tend to suffer from a "too-active imagination" when reading about the suffering of other people in the news, and vividly imagining the events described. My solution has been to stop reading the news. When you're faced with something terrible and you're not doing anything about it anyway, just look away. Defeat the implicit LW conditioning that tells you looking away from the suffering of others is wrong. It's wrong only if it affects your actions, not your emotions.