False accusation is a common anxiety in the West and other cultures. Breaking the social contract, etc.
TBO's analogy was off point, as police officers operate off of different levels of reason for detaining someone - the oft-mentioned stop and frisk, reasonable suspicion, etc. continuum. I mention that as it is relevant to the point he seemed to be making - that the woman wasn't necessarily 'wrong' in her actions - she was exercising her authority, albeit erroneously. I'll try and come back around to that transparently by the end of this post.
Could have left the store, I can imagine and understand why a person would not. Could also have 'prepared' your firearm for the officer - I can even more clearly understand why a person falsely accused of shoplifting would not decide to pull a gun out and dismantle it. Could have called the police and stated that you were the subject of a recent call from the store, looked forward to explaining the situation, and that you were armed under CWP, and that you were interested in alerting the responding officer to that and your benign intent - again, can clearly understand why a person would not choose to do that. Could have gone to your car, placed your pistol in the trunk and waited. Again - you know.
As far as hiring a lawyer, I recommend calling your local Bar association - get a free consult or two and then decide. The things you mentioned you might bring suit for don't seem likely to bring any money damages that I am aware of. What are your damages? Defamation suits are very specific, as are emotional distress suits. You made a reasonable move by notifying the management, sounds like they have promised response - follow up with it. Maybe you'll get a free pair of shorts out of it. Tell them what you want, why you're asking for it/think you deserve it, and the lengths you're willing to go to get it - for real. Maybe in the end, you'll be able to write this up to a funny experience - "how I got a free pair of shorts". Familiarity breeds acceptance - now you've been through one experience with LEO response to you carrying. Next time, it will be less exciting for you.
Consider focusing your efforts on you getting something you want, rather than giving somebody something they don't want. Go for a couple free pairs of shorts, wear them into the store and thank the lady for them if it makes you feel better. If she works management, cash register, and security at a store that sells $5 shorts, perhaps she has some struggles that prevent her from acting rationally or reasonably. She could be on work furlough for all we know. Did she ever prove she was an employee of the store, authorized to make the call?
If you go trying to get somebody fired to show you're more powerful than she is, chances are she already knows it - she was trying to show her power in 'her' store, and already she knows she wielded it improperly/erroneously. If she gets fired or chastised from the boss, she'll suffer more - does that give you anything? Perhaps it does - perhaps it's what she needs to change her tune, and you'll fell better knowing you saved the next unsuspecting sap from this humiliation - but make sure you're deciding what you want, and not reacting to her.
This is not legal advice. In fact, it's not advice or a claim of fact at all - it's just some simple comments.
Madness is like gravity; all it needs is a little push.