That is savvy question, but the short answer is no you could not.
Under IRS rules, you can't “cherry pick” by converting just your after-tax contributions to avoid taxes. Instead, you need to determine the % of after-tax contributions across all your IRAs and then use that % to determine your taxable portion. In order to calculate this %, you need to total all balances in your IRAs. You do get to exclude your spouse's IRAs and any inherited IRAs though.
Here's an example. You have $100,000 eligible for conversion in two IRAs. One account has $85,000 in pretax contributions and earnings; the second account has $10,000 in after-tax contributions and $5,000 in earnings (pretax), for a total of $15,000. If you want to convert $10,000 this year, the taxable income on this amount would be $9,000. That's because 90% of y our total IRA is pretax contributions and earnings.
Consider converting some every year to cut your taxes.