I've tried a million things, and it seems like this cheap solution wasn't just the best, it was the easiest too. Here's what I used:

Bar Keepers Friend - https://amzn.to/3J3Socx
Grout Brush - https://amzn.to/3ZARN7O
Clorox Bleach Cleaner - https://amzn.to/3IMDKoP