"I can convert $16,740.07 of the funds in my traditional IRA to a roth with no tax owed. Converting the full amount of $17,897.40 will leave me with about $1k that is taxable."
It sounds like you still have errors in the calculations that you've done. If your basis is only $16,740.07 (I not sure how that might have happened unless previous conversions were partially taxable and you had a nonzero balance in traditional IRAs at the end of some year) which is less than your balance in traditional IRAs, any conversion will be partially taxable. You cannot convert just he basis; any conversion is a proportional mix of nontaxable basis and a taxable remainder. Unless you convert the entire amount and you have no balance in traditional IRAs at year end you'll have some basis remaining.
