I guess I come to this from a different place. My boss is the ONLY person whose respect or approval I care about, because I like to eat and have my home heated. If you work for satisfaction, and don't need the money, good for you.
We're not talking about social situations here - it's a job. This isn't personal, it's business. You can't be forced to continue a job if you don't want to. You can quit, any time you want. That being said - "Amends" isn't just offering an apology, it means compensating or making up for a wrongdoing. There's nothing you really can do but offer an apology, but understand if the business was left shorthanded at the holiday, that doesn't 'amend' anything.
It's kind of laughable that your employer to wants you to sign a non-disclosure agreement after you've quit. That's the sort of thing to take care of before they hire someone. [shrug] Too bad for them.
The only thing the employer can do is tell a potential boss that you're not eligible for re-hire. In the current US economy with really low unemployment, I suspect finding a new job, if you want one, won't be difficult.