No, you cannot decide to use all the basis of your Traditional IRAs in a single year.
If a distribution is made from a Traditional IRA and you have a basis in any of your Traditional IRA accounts, the distribution is always considered to be a mixture of pre-tax and after-tax funds over all of your Traditional IRAs. It does not matter whether you are converting the distribution to a Roth IRA or if you are doing something else with it. You need to enter the total value of all of your Traditional IRA accounts for the calculation to be accurate.
You may also hear this situation referred to as the 'pro-rata rule'.
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