Jenna C. answered 04/26/19
MEd in Instruction & 7+ Years Teaching Writing
The short answer is that it doesn't matter. To expand on that, "figure out" is generally used as what the Cambridge Dictionary calls a "phrasal verb," meaning that it's most commonly written as a phrase with the two words together, but it is generally acceptable to insert a noun between "figure" and "out" as your proofreader suggested.
If you're concerned about the grammar of it, then the safest route might be to stick with your original version, but since both ways are correct, and it's being used in a piece of fiction where you get to bend the rules of grammar a bit to suit the story you're telling, you can choose either version.