Legal Question in Technology Law in Florida

You cannot unilaterally impose new charges that are not provided for in your contract. Your remedies are probably limited to the amount due plus interest and court costs, though you may be entitled to recover attorney fees and/or other sums depending upon what the contract says. Depending upon the facts, a different way of calculating damages may be more appropriate.

If your customer deliberately misled you into doing work you would have refused if he had given you better information, you might have a claim for fraud. A successful fraud claim could entitle you to punitive damages and perhaps to other relief. But it still would not entitle you to make up a daily "licensing fee" and force the customer to pay it.

Your situation is different from the songwriter's that you mention because there are collective bargaining agreements (CBEs), which the major record labels have all signed, specifying the minimum amount the songwriter must be paid and setting forth the penalties for a breach. Those contracts also protect non-members of the unions, though not always the same way as members. There is no such CBE for web developers, and even if there were I doubt this particular customer would have signed it.

Consult with a lawyer in your area about your rights. And bear in mind that your customer could file for bankruptcy and thereby eliminate much or all of his debt to you. You should take steps to protect yourself before that happens.