I know that だり...だりする is used to list verbs from my genki I book, but I knew that wasn't what was occurring in my sentence. While looking for aid to figure out what the だり in the last sentence means, I found this answer here. I still can't figure out what the だり is doing in the last sentence.
Therefore, how is the だり affecting the 悩ん in the last sentence?
体力も神経も使い果たし、疲れ果てて泥のように眠る毎日が続く。余計なことを考える[暇]{ひま}もなければ、夢を見ることもない。やがて、そんな生活に慣れはじめると、今度は物事をじっくりと考えることが苦痛になってきた。その時々の課題をクリアすることに、全力で取り組んでいる間は、何も思い悩んだりせずにすむ。
My translation attempt:
Using up my stamina and nerves, the wet dirt tires me out so that I wish to lie down every day again and again. Neither time to think to unnecessary things, nor things to dream. In the end, that sort of life when I start to grow accustom to it, now without rushing everything, my thoughts gradually become agony. That at times clearing the task, for all my power is a period of working hard, without worrying about anything among other things I feel at ease.