Hints: Ministry of Word Searches

Getting started:
These are word searches, but they’re not entirely conventional. However, it seems like the same nine words keep appearing all the time…
Finding a minimal grid:
You don’t have to be perfect to read the message, but it may help to know that you can fit all of the words on a single row, column, and diagonal. The Chinese remainder theorem might be helpful.
Graham’s Number ID is not accessible using the puzzle applet, and nor is any grid that exactly matches it, so you’ll need to make your own. See https://oeis.org/A240162 for help doing this.