Even if you do make that full Estimated Tax Payment in the same quarter as the conversion, if that quarter is the 4th quarter (or possibly also in the 3rd quarter), you may still get hit with a penalty for underwithholding. I know it makes no sense at all, but the IRS treats Estimated Tax Payments differently than they do tax withholdings.
For the reasons already mentioned, the withholding method is not always optimal for Roth conversions, so you are usually left with the Est. Tax Pmt method. The conversion amount is considered to be spread evenly over all 4 quarters of the year since the conversion date is not reported to the IRS and most software doesn't seem to be able to get around that. As such, 1/4 of the conversion amount is assumed to be in each quarter, but your Est. Tax Pmt was in the 4th (or 3rd) quarter. This means you look to have underwithheld in the earlier quarters. FYI, if you did use the withholding method, it too would have been spread evenly across all 4 quarters and there should be no issue and no penalty. An IRA distribution would be similarly problematic if you paid by Est. Pmt, but averted if you used withholding instead.
The only resolution seems to be to opt to Annualize your income using Form 2210.
