I don't think we're talking about the same problem here. If the day comes that Tethers are proven to be insolvent (because there isn't actually a USD in reserve for each Tether in circulation), moving quickly won't make a damn bit of difference. You can't quickly unload an asset when there is no taker. Somebody will be left holding a big fat stack of nothing.
I don't know what's going on with Tethers, honestly, it's not something I've followed very closely; so this may not be a problem at all (and if it's not, I would assume the people involved would be eager to get an audit done and results published so the money train can keep rolling). I'm just saying that unless you believe strongly that Tethers are backed 1:1 by USD, it would be irrational to hold Tethers, even for a short time.
I found it worrying that when the guy they interviewed tried to move his Tethers to another exchange, he couldn't find enough takers (and Bitfinex wouldn't let him exchange for dollars either). So, the argument that Tethers trading at roughly $1USD across exchanges is "proof" that Tethers are sound is shaky, at best. If you can't sell more than a handful of Tethers without crashing the market for Tethers, it's not actually the market setting the price. Something else is going on...something that would be illegal in a regulated market.
You'll be able to unload, but basically only into other crypto. Exchanges that deal with crypto will see crypto prices skyrocket, then shortly collapse, as people buy BTC or other coins then try to move to other exchanges to sell for real USD.