Hi Ryan,
If you just want to look at category permissions without clicking the categories in the backend you can do so by using SQL queries in your database.
However, before you build the queries, you need to know what data you want to retrieve out of the database tables. If you want us to draft a query for you, can you perhaps give me a brief overview on how you would like to look at your category permissions?
For example:
By referring to the screenshot, can you tell me whether most of your categories utilizes the "Assigned Joomla User Group" privacy setting? If that is so, then would you want to just view categories under that privacy setting and review the user groups permissions from there?
Let us know how do you want to verify your category data so we can provide a draft query that could achieve this. Thanks.