"In the bigger academies, which are 141 approved"
141 is a joke. It's FAA bureaucracy at it's finest. It's overly restrictive and puts unnecessary constraints in the training process.
You can find CFI's at some FBO's and flying clubs that are superior to a big academy. Sometimes retired airline pilots or highly experienced pilots just doing it for fun. Sometimes not. You gotta shop around.
141 is no guarantee of anything, I think.