Much debt - a lump sum to use - where should I put it?

I have 6 credit card debts totaling around $43,000, and a first and second mortgage. I have gotten an inheritance which will pay off MOST of my credit card debt, but not all ($34,000). I know about the debt snowball, where you start paying off cc balances from smallest to largest. I really want to refi my first and second mortgages into one - at a lower interest. First mortgage is around $50,000 at 6.25% and second is around 42,000 at 9.25% with a balloon payment in 14 years. I was late on 3 of the cc payments for a month or two, so I'm concerned about my credit score for the mortgage refi. I want to use this inheritance to the best advantage. I haven't looked at my credit score for awhile. I was going to wait until I used this money to pay things off and then check it. Up until I was late on these cc (BOA and Chase raised rates & payments!!), I was on time with everything, so I think my credit score up until then would be okay - now I'm not sure what it is. Should I totally pay off my largest cc debts? (which would leave full balances on the lower cc debt) Should I spread it out and pay a portion on all of them? I've heard that cc's should be paid down to 90% of available credit in order to raise my credit score. My inheritance isn't enough to pay down 90% on all. I would just do the debt snowball, but I want to raise my credit score as much as possible in order to get a good mortgage refi. I'm a little lost - any suggestions?