You aren't paying taxes twice. Your distribution is a mix of nontaxable basis and taxable amounts from your traditional IRA. Future distributions will also be a mix of taxable and nontaxable until you've received distributions of all nontaxable money from your traditional IRAs. This will not occur until you have distributed all of the money in your traditional IRAs and no taxable or nontaxable amount remain in any traditional IRAs at year-end. So yes, if you had no money in any traditional IRA at year-end the result will be that your final distribution will include the remainder of your basis.
Remember that for the purpose of determining the taxable amount, all of your traditional IRA accounts, including SEP, SIMPLE and rollover IRAs, are treated as a single account.
