In otc, you can short on the offer all the time. In the nyse, you can sell only market (a trick is to buy 100 shares to uptick it, and then empty your position and get short, though you usually need 2 accounts for this, but it isn't necessary on anything even semiliquid)Besides, by the time the market is tanking you should already be short and covering into the drop. That way, when the selling slows, you can be averaging into your long and sell that and then get short again into the bounce strength. If your position is longer term, a few ticks won't matter in getting short anyway.
As for the large sell orders. Lately, with the exception of biotech where a fund blew up, there haven't been any major large individual sellers in most names. There just haven't been any buyers, so you really have to hammer a stock down to find a bid.