I would be wary about being completely open and honest about such things at exit interviews. There is nothing to gain for the ex-employee personally at that point in time, and everything to lose by 'burning bridges'. You never know when a few criticisms (even if they are accurate and correct) will come back to haunt you.
At the exit interview, the main thing is to do what is best for yourself. If you really want to change how the company operates, stay on and apply gentle pressure or guidance. Criticism presented at an exit interview will 99% of the time come off sounding like sour grapes (unfortunately).
This is totally right, you absolutely want to sugar coat it. Don't say "I'm leaving because I hate bill". But for everyone else's benefit you can drop in that this new place you're working for gives you the flexible hours you require and is paying you more money.
The point was more, "if you're unhappy, find something new." You don't owe anyone anything, and if they can't figure out how to incentivize you into staying, you shouldn't. It sounds like old manager had a good grip on it and new manager does not, in this particular case.
Yup, important communication is often best when informal. For forms, official interviews and the like, carefully protect your goals. But be creative in considering how you can educate the other party.