A thought I picked up from Ryan Greenblatt.
Even if we're probably doomed, the expected value of trying hard to improbably save Humanity Ascendant is still huge -- on the order of saving a planetary civilization in expectation, even if you're not saving a cosmic civilization in expectation.
Doomy emotions can be instrumentally useful … when you can potentially affect the thing you're being doomy about! Emotions just aren't instrumentally useful when they're about things that are out of your control. In that case, your feeling bad doesn't help anything. If you've just updated your world model in a very doomy direction, feel that hit … and then go right on EU maximizing in the world you live in, in the normal way!
(Worrying about fixed amounts of doom is like worrying about sunk costs.)