Still, I wouldn't trust them to send a transaction in a timely fashion at all considering all the complaints of delays recently.
I say just suck it up and use Bittrex. Their fee is 0.001, and it's not too bad when you're using normal amounts.
Till now I didn't face any problem with Poloniex when performing a withdrawal and at the same time withdrawal fee is also very low.
Here's just one example of someone talking about an extremely slow withdrawal from Poloniex (8 days).
Closing the trollbox makes it impossible to access the support, because they almost don't exist. No withdrawals from an exchange should ever be slower than a few minutes unless they suspect that you're doing some shady activities and can reasonably justify it.