I agree that credit karma is a very useful app. A number of years ago, I had a bunch of credit cards that I used responsibly to build my credit, but when I lost my job, I used them to float me through my unemployment. Needless to say, I maxed them all out and found myself making about 7 minimum payments each month totaling about $200.
I ended up calling a credit counseling service(the number was on one of my bills). They negotiated lower interest rates on my cards with the credit companies, they consolidated the debt, and I paid them my one monthly payment. My debts were paid off in three years by paying $20 extra dollars a month. Who knows how long it would have taken otherwise.
My point is, maybe you could call your credit companies and ask them to lower your rates so you can put a dent in your principal balance quicker. They may do it because they realize you are attempting to settle your accounts, and it may sweeten the deal on both ends to make those payments via direct deposit. They will feel more comfortable with that arrangement, and you just have to remember and account for your fixed direct deposits.
I had to cancel all my cards for the service, which gave my score a slight hit, but if you wanted to keep them activated, your score will improve once you are down to a debt of 1/3 of your limit. A great trick I learned for curbing credit card use is to put one in a ziplock bag, fill it with water, and freeze it. That way, if you decide to use it, you have time to think about what you are doing while it thaws.
As far as the existing late payments go, I don't know if there's anything you can do but wait. A lending agent at my bank once told me that, when looking for a refinance(I'm assuming mortgage loans would be similar), they look at the current mortgage loan for the span of a year. He said to make all my mortgage payments on time for a full year, and I would have a lot more options.