I am still managing to meet my monthly payments

No, you can enroll in a debt management program anytime when you are facing financial problems. You will get the benefits of lower interest rates from your credit card companies. This program will not let you get behind in your payments. Speak with a debt counselor for some easy repayment options

debt settlement companies are the ones that require you to be a certain amount of time behind on your payments. I think that's because they can negotiate a settlement better.

Just be careful if you do go with a company that you payments don't get behind. Since you are paying money to the debt management company, and they are paying your creditors you don't know for sure when or if your payments are being sent. Since you aren't behind yet, you probably don't want to get behind. I would ask them when your payments will be sent, and maybe be prepared to send them yourself for a few months until you know for sure the debt management company is sending them on time.