There are a lot of different factors in your question for me to consider and some facts are missing that would allow me a more complete analysis. I don’t know the extent of your financial means, which would allow me to more accurately weigh all of your options and make a formal recommendation. Lacking that type of detail, I will make some assumptions and then some general observations.
It is my view that life often consists of weighing pluses and minuses of various options available and trying to find the best possible one, as opposed to working to implement some ideal solution. In your case, you seemingly don’t have the ability to maintain your payments to American Express and also take advantage of the attractive, low-dollar settlement offers from your other creditors.
Consequences of Default
You asked what would AmEx do, if you break the agreement. It is my opinion that American Express is going to pursue collection efforts against you, if you default on your agreements and can’t work out a satisfactory arrangement. Defaulting on your American Express will likely lead to your not being welcomed back any time soon as a customer. How valuable to your business is the use of your AmEx card? If it is crucial to keeping your business operating (and you wish to keep your business going), then breaking your agreement with AmEx would harm your business.
You also asked if AmEx would agree to a lump sum settlement. You certainly can approach them and ask. Again, make sure to consider the implications of this on your business, as they may not want you back as a client if they settle your account for less than you owe.
How Much Do You Owe?
You didn’t state how much you owe the AmEx and how much you owe the other creditors, which certainly is an important factor in making the best decision. The less you owe AmEx and the more you owe the other creditors, the more sense it makes to break the AmEx agreement and take advantage of the settlements offered by Citi, B of A, etc.
Regarding your other creditors, what did you tell them to induce them to offer a settlement? Most creditors will not consider a settlement unless the account is severely delinquent. Essentially, the creditors only settle for less, when they feel that less is the best they can get.
It is not clear to me how you could afford to pay lump sum settlements to so many creditors in a short time, but not have the ability to maintain your payment agreement with AmEx. It may be related to the size of your balances with each creditor. If you can liquidate an asset or borrow the money from someone to fund your settlements, it is likely a good idea to do so. If, however, you only can satisfy some creditors and other ones go into default, you expose yourself to the risk of collection efforts, legal action, judgments, wage garnishments, and bank levies.
Garnishment and Levy
If you have a job where you receive W-2 wages or receive 1099 income from someone who contracts for your services, a wage levy can be devastating. I recommend that you review your state's collection and exemption laws, the laws in your state that govern how much of your wages, if any, are subject to garnishment and what protections your bank account has. This way, you will have a better understanding of the risks you face and can make a more informed risk/reward calculation.
Meet with a Bankruptcy Attorney
Lastly, if you owe a lot of money and are in a serious hardship, you should speak with a licensed bankruptcy attorney, to see if you can discharge your debts or if any type of bankruptcy would improve your position if any creditors choose to become very aggressive.