Well, I think they should not at least allow deposits without verified account (for new accounts, that cannot withdraw anything without verified account). So if you have new account, you wouldn't be stuck in this really bad situation where you just wait and hope for the best.
I think Bittrex want people to keep depositing, then lock up their funds with this verification scam.
Other exchanges in the US under the same AML/KYC still allow limited unverified withdrawals, eg. Poloniex.
Bittrex are up to something, and it smells of no good.