The IRS language is pretty unclear in Pub 936, but one thing it does clearly state is that the interest rate method can only be used "if at all times in 2021 the mortgage was secured by your qualified home and the interest was paid at least monthly."
In your case, assuming you did not carry all three mortgages for the year, I would use the monthly statement method if you do not feel comfortable with TurboTax's method of calculation. The easiest way to calculate that is to take the outstanding mortgage principal in box 2, multiply it by the number of months you carried the loan, and divide by 12. For a better and more accurate result, you can actually refer to your monthly statements, as your principal will decrease each month.
To get TurboTax to use your calculated number rather than have it calculate using the average of the first and last month only on outstanding loans, you can mark every loan as outstanding by answering Yes to Let's see if this is the most recent form for this loan. For Outstanding mortgage principal in Box 2, you would enter your calculated amount for each loan. You would enter this again when it asks for the balance on January 1, 2022.
