You can override the TurboTax calculations using the instructions above if you are not comfortable with how TurboTax calculates the average balance. The IRS certainly won't trouble you if you are deducting less interest than you would be eligible for.
I don't disagree with your interpretation of the average balance. Intuitively, it makes more sense to me. IRS Publications can't be used to justify tax positions, you would have to dive into the actual Internal Revenue Code (which I don't think is any more clear) and any previous treasury regulations or rulings to see how they have interpreted this in the past.
@jxman
