Do you really believe that someone who felt happy despite knowing about the state of suffering in the world would be more strongly motivated to reduce suffering than someone who felt a great sadness and a burning desire to stop it every time they thought about it?

Sadness and burning desire are not in the same bucket. Sadness doesn't make me want to do anything at all. It quickly leads to depression, which is about the most unmotivated it's possible to feel. Certainly when I'm happy, I'm more motivated to do something about saddening things than when I'm actually sad.

Now, anger is an extremely motivating emotion that might work better for these purposes...