I got this now ... let's hope it's true!!
"We are actively training new personnel and streamlining our processes to better handle the increased demand. Specifically, in the next week, Bittrex will be more than doubling our current support staff to handle the growth. The hiring of support agents will continue until we can provide the support our customers expect."
They are verifying accounts regardless. So you should be fine. They are just extremely slow and unprepared. Yes they are unprofessional but at least it doesn't seem like a scam, at least apparently.
Woohoo, I finally got verified! After 4 weeks! Seems indeed that they were just very unprepared ...