You are correct that if you only make an estimated payment, you can be subject to underpayment penalties for the previous quarters. I believe the penalty is based on the actual tax owed, not including a fudge factor for what the minimum correct estimated payment would have been.
To minimize the tax owed, you can do one of two things.
1. Pay the estimated tax in the quarter that you do the conversion, and then include form 2210 schedule AI with your return. This is the annualized income method of calculating the penalty, and it will show the IRS that your income was uneven and your payments in each quarter were correct for your income in each quarter. (Turbotax may not automatically trigger the penalty interview, but you can manually open the interview if Turbotax does not automatically run it for you.)
2. Have the tax withheld from the conversion. Withholding is assumed to be spread out over the whole year, just like income, so a penalty never evens comes up. For example, if you want to convert $10,000, have them withhold 22% and send you a check for $7800. You then send a check to the new Roth for $10,000 (by making up the difference from the funds you would have used to pay the estimated taxes). This is an indirect rollover, that you can only do once per year. The withholding will appear on your 1099-R.
Or, you can inquire of the receiving custodian if they will assist you in doing a rollover with withholding. For example, if you tell them "I want to roll over $10,000 but have withholding, can I have my plan send you $7800 and then I make an electronic payment of $2200 and we call it a rollover of $10,000?" I'm not sure this is possible but you can ask. Having withholding eliminates the need for a penalty calculation.
