After a lengthy discussion on a veterans' forum I belong to, I called American Consumer Credit Counseling. That was the highest-rated one among all of those in the discussion. I consolidated five high-interest credit cards that I had trouble making minimum payments on. I was never late and always made payment, but the terms sucked and I owed a total of about $28K. The interest rates were knocked down to roughly 5% from around 20%. Only one lender (BOA) placed a remark on my credit report...something like "this account has always been paid on time, but is being managed by a credit counseling service." I paid off those debts in four years and had zero issues. I was able to get an emergency credit card, a car loan, and even a mortgage during that time, and my score did not seem affected by my consolidation.
I realize that many of this sort of companies are in bed with banks to some extent, and I was very very skeptical, but my experience was positive.
I have no connection to ACCC except being a satisfied former customer