Sounds like a nightmare! I am very weary of exchange wallets. I always transfer what I want to trade directly to the exchange wallet, do my trade, then get my coins the heck outta there.
A lot of these companies are being run by a very small team of inexperienced, shall I say, children with no real work ethic or understanding of good customer service or business practices. Then the company blows up huge and they are left completely lost as to how to deal with the sheer customer volume. Or they get hacked like the recent Nicehash event. I would not want to be those guys right now!
I am following your advice to a tee now... agree these guys are over their heads. Hopefully with all the money rolling in they can get some professionals in there.