That sounds like blackmail/extortion. I'm not a lawyer, but the first amendment should protect you pretty well from merely making truthful accusations, but once you threaten money in exchange for not making them it could be construed as a very serious crime.
Avoiding bad PR is one of the reasons most settlements have non-disparagement clauses, usually paired with a confidentiality clause that says you can't even talk about the settlement (and therefore you can't mention or imply the existence of the non-disparagement clause therein).
"Hey thought you should know, my 'security' company is currently for hire for businesses around town. We heard through the underground grapevine that a lot of folks may lose some product in their bodegas next month. Anyway, nice to introduce you to my 'security' business -- have a great month!"
If you revealed that your true intent was blackmail, and that's what this is, to your lawyer or anyone else then I imagine the intent in combination with the act is enough to nail you.
Give me money or I will tell the public that you did me wrong -> not extorsion
Give me money or I will tell the public that you did someone else wrong -> extorsion
I believe that the litmus test is whether you are entitled to a compensation or not.
Either can be defamation though.
In my previous classification it would be extorsion to say "pay me or I will add those things to my accusations" but not to say "pay me or I will drag you in the mud as much as possible", that is it would matter whether you keep them bundled together or not.
Why do you imagine non-disclosure agreements are standard after an out-of-court settlement? It's because "pay me or I'll badmouth you" is essentially always one of the implied threats.
You can call it blackmail if you want (and I'm being deliberately glib here, because I also think it's at least blackmail-esque), but your lawyer and the company's lawyer will absolutely understand that this is how things are done.
You don't do this out of the goodness of your heart to inform other people how bad the company is, you do this purely to maximize the probability of receiving any sort of compensation from the company. Most people (?) would only consider this route if they genuinely feel that the company has egregiously wronged them, because it's a big, low-probability-of-success pain, and airing dirty laundry is easier and often more cathartic.
If you have already decided that informing other people is more important to you than a settlement (or have concluded that the effort is not worth your while), then fine, you've made a different decision, and perhaps the commons are better as a result. But if you decide to air the dirty laundry, you'll usually lose the ability to change your mind later.