Getting a Mortgage with credit card debt?

My credit score is about 605. I have several credit cards with balances near the limits (about $ 45k), but no other credit problems. My wife’s credit score is about 640, with little debt, but some delinquent accounts from a few years ago. If my wife got a personal loan for, say, half of my credit card debt, how long would it be before my credit score went up, and how much would it be likely to go up? We want to buy a house soon (next month or two); would it be better to apply for a mortgage now on my wife’s credit, or try to get my credit score up?
Montly income (gross): $ 7300
My wife’s delinquent accounts are paid, they’re just still on her credit report. All of her recent accounts are up-to-date.

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