I bit the bullet and did "pay only the required fee of 0.00001000 BTC."
-Sent at 5:13PM 6/5/2017.
-Amount: 0.01128000 BTC, approx $30 according to BTC-e's estimate at the time.
-Fee of 0.00000226 BTC [0.225 kB] was attached. (less than a penny).
-For this transaction, 3 confirmations are required.
I'll update you when, if ever, the transaction is confirmed. Good night!!!
I doubt that transaction will confirm as that fee is way too low.
I recommend you take a look at
http://bitcoinfees.21.co/ and you can see the suggested fees based on current levels of unconfirmed transactions. Each block takes on average 10 minutes, so 25 blocks would take on average about 250 minutes but could end up taking a lot longer as well.
Unfortunately, bitcoin fees are absurdly high at the moment so hopefully they can determine a good method of reducing them so they aren't so costly.