Liberty is a p141, VA approved school. But they are a rip off.
My msg, although maybe lost in a wall of text, was merely that anyone looking at GI Bill funded college programs should really research the schools they may be interested in to ensure they are getting quality training and minimizing both out of pocket costs and training duration.
The handful of private colleges I researched all maxed TA funding and charged the maximum permitted by the VA for flight training (likely the reason their aviation programs were Yellow Ribbon Program capped). I assume State College options would likely be more reasonable and a better value.