Great news!! We found this answer in IRS Publication 590, Individual Retirement Accounts:

Tax treatment of a rollover from a traditional IRA to an eligible retirement plan other than an IRA:

Ordinarily, when you have basis in your IRAs, any distribution is considered to include both nontaxable and taxable amounts. Without a special rule, the nontaxable portion of such a distribution could not be rolled over. However, a special rule treats a distribution you roll over into an eligible retirement plan as including only otherwise taxable amounts if the amount you either leave in your IRAs or do not roll over is at least equal to your basis. The effect of this special rule is to make the amount in your traditional IRAs that you can roll over to an eligible retirement plan as large as possible.

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