One thing about part 61 is that you’ll be doing most of the ground school work on your own, just like at ATP. If you can’t keep up because you’re not good with non-structured programs or you can’t get the help you need to explain some of the information you’re going to end up feeling frustrated. Frustration can turn anything you’re trying to dip your toes in into resentment and you’ll end up abandoning it and wasting money.
At the very least start with part 141, it will walk you through the process, you’ll have instructors who will be there for you to explain things you might have already read. So it’s a like a double lesson. People are different, but nothing wrong with going over the same material from a different perspective. If anything, you’ll be a safer and more proficient pilot.
Some instructors also have enough experience to give you a lot of helpful anecdotes you won’t get from a 61 program.
Side note: Can taking a leave of absence reflect badly on you at your FA job? If so, why the rush?
ATP has a nice turnkey program, but remember that multi engine training is in Texas (or is it FL?) for a few weeks and once you graduate, you can’t request a base airport or city where you’ll be an instructor racking up hours.
It’s at ATP’s discretion and you’ll have to bunk with 3 or 4 other roommates. That might be something you’re used to as an FA (I don’t know), but if it’s not, then it’s something to take into account. The older we get, the less tolerable it is to have roommates.
I can’t help much with the flow programs since I don’t know much about them. But hopefully this information can come in handy in making your decision.