Same situation myself[0] except credit score 775, and I could get a mortgage, but, no matter what % the down payment, the interest rate wouldn't be below 5%, at a time when conventionals that were Fannie-flippable were getting under 3. (This situation exists because Fannie buys without consideration for long-term interest rates or the impact of a higher down payment after some threshold.)

[0] https://news.ycombinator.com/item?id=31220794