Google Sheets highlight a column if a checkbox is checked and also matches an input, applied to the whole row

So I don't know what to call this so that explains my title, but I have a solution that works, except I want to have this apply to a row of checks so I dont have to duplicate my conditional formatting for every column. This is for a game called Phasmophobia, and I wanted to make a sheet I can select checkboxes to show potential answers for the game. Here is my example:

Basic View

Highlighted View

My conditional formatting function is =if(($C$3=TRUE)*($C6=$C$2),true,false) So what I want is to check if the checkbox is TRUE, then highlight rows that has the corresponding data in the row. This formula works as intended, my only issue is I want to make this formula work for all the checkboxes in one formula, so I don't have to make 20 conditional formatting, because on top of the current formula I have plans to modify it to have 2 additional conditions to highlight for, for example if the checkbox below the top row is checked, then cross off instead of highlight the same rows from the first formula, and to cross off rows which don't contain the correct information. If this isn't possible I can just suck it up and make the conditional formatting rules manually, but I know this game has intentions to add more things to track and I wanted a simple "paste in and it works" solution.

P.S. I only have it comparing the ($C6=$C$2) because it makes it possible to remove the need to keep the columns all lined up with the checkboxes, but I can remove that in place of a "istext($c6)" check.

Link to a copy of my sheet: https://docs.google.com/spreadsheets/d/1I1be4O6BH4S0HscRsY-1NFPOyVm_8F7zr642Bbu28Qg/edit?usp=sharing