I am curious, why do you have 3 different credit repair companies? I would think that their services would be overlapping somewhat when they are disputing errors on your credit report.
As far as credit scores go, there are a handful of lenders that MIGHT entertain your scenario with those scores. Big maybe because those types of lenders are accepting a bigger credit risk than traditional 640+ FHA lenders so they would ask for at least 10% down and condition the heck out of you.
In my opinion as a lender, I would work on getting your scores up. Pay down your credit cards, save your money and don't take on any new debt.
No Down Payment loans include USDA Rural, VA, and perhaps owner financing. There may be others that are not as common.
Taking over Payments?
There are very few "non-qualifying assumable mortgages" out there.
You will [most likely] be required to qualify to assume the loan.
If you try something like "Subject to the Mortgage" or "Rent with Option to Buy", please see a Real Estate Attorney for legal advice. Have the Attorney draw up the Contracts and other Documents.
Please speak with a Lender or Lenders regarding this situation. You may wish to call the Bank or Credit Union where you do your checking and savings, and tell them you want to talk about a Mortgage Loan.
Best wishes to you,