Translating "整理し" > Trying to translate this, for now I have > At such times, our firm first organizes and visualizes what the problem is. But I'm not comfortable with the idea that the firm "organizes [...] what the problem is". Should the idea of "" be on its own? For example: > At such times, our firm first organizes the facts and visualizes what the problem is. I know "the facts" is not in the Japanese, but it seems assumed in the context of facing a problematic situation.

Your understanding of complementing it with 'the facts' is practically fine.

In Japanese, can be intransitive and considering it as on its own is one possibility. Another possibility is to assume some implicit object. As I said, 'the facts' is fine, but in Japanese it is idiomatic to say , meaning analyzing the problems into factors. So, though virtually the same as your translation, it more literally means 'we analyze and visualize the problem(s)'.