Little off topic, but bitstamp required ID verification for BTC withdrawal too, correct?
Yes they do,withdrawing/depositing cash AND bitcoins require complete verification with an ID and a proof of address.
Do you have any experience in withdrawing EUR instead?
No personal experience but considering some posts on this forum that claim they "Finally" received EUR payments without mentioning the length of delay,also since the MTGOX problem is generally "fiat money" after some of there accounts were frozen I doubt it would be much better than USD withdrawals.