Any other debts? Car payments, child support, credit cards, student loans, etc.
At $350k, 30 years, 4.375% (probably can do better), with 20% down, and using 2% annual property tax and insurance rate, your total monthly payment is $2330.83. At $65k, your DTI is 43%. If she has no other debt, with her score, probably a go.
Otherwise, can you look into restructuring any of her existing debts, to become yours? Definitely think best course if to only document her, at this point in the game. You can add yourself to title at closing.