$13,000 used to pay off student loans @ ~5% = $325 interest savings

Using an awards credit card promotion to pay the taxes via Visa gift cards to reduce my effective payment fees to less than 1% = $130 in fees (rounding up to 1%)

Cash back on the credit card gets me approximately 2% of the $13,000 "purchase" =  $260 cash back

Credit Card promotions net me 80,000 airline miles which I'm redeeming for a round trip flight to Europe in business class.

So, decreasing my withholding is netting me $455 and a flight to Europe that would cost $3000+ were I paying cash for the flight (I'd never actually pay that much for business class, so it would disingenuous to say that it was actually a $3000 benefit, so lets discount that to $1000 for a total of $1,455 benefit).  For me, that's worth not making an interest free loan to the government.