Mario,
How are your other debts? The following is not advice but food for thought based on personal experience.
As a new couple ready to start a family, we desperately wanted to buy a home. We discovered that mortgage debt has a maximum allowable DTI ratio and that there is a separate, higher, DTI for overall debt. What that means is that, if you have no other debts, one thing you can do is get a personal loan from a bank (or... a cash advance on a credit card...). Don't spend the cash. After three months in your account, it seasons and the banks do not consider it as "borrowed for mortgage" purposes.
Example: Say you make $100K per year. I believe FHA is now allowing a maximum DTI of 45%. That means that your debt payments can be as high as $3750 per month. However, the maximum mortgage DTI is 38%, or $3167 per month. The difference between the two is the maximum that you can be paying per month for car loans, credit cards, personal loans, etc., and still qualify for the maximum mortgage. $583 per month.
With your high credit score, you can probably borrow $20K fairly easily and still have payments under $583 per month. Wait 3 months after borrowing so that you have $30K sitting around in a bank account for 3 months and... problem solved.
Again, I am not "recommending" this. But, this is how our family bought our first home.
