Those sources don't force you to take anything on faith. Rather, they encourage more research. This may require doing something other than watching flat earth youtube videos...gasp!! Good science requires you to go out and prove data is corrupted and/or faked. Simply claiming something may have been corrupted and/or faked is not enough.
So, science states that small mechanical gyroscopes do not move with the earth's rotation. Therefore, a small mechanical gyroscope not moving is not proof of a flat earth. All those videos of small mechanical gyroscopes not moving are misleading, a common tactic in flatland.
Maybe you should investigate things in real life, rather than taking on faith everything they tell you in flat earth videos.
Naaah, that would would be actually doing something. Better to sit back and watch some more videos that reinforce your delusional world view. Remember when the central tenant of your theory is a conspiracy, its not scientific.
Cheers!