The problem with how this is presented is that the last BIG drop in temps was not 13,000 years ago, it started over 100,000 years ago. That “sharp” decline appears to have taken around 10k years, and then after that it gradually (with some fluctuations including the cold snap discussed in the article) got even colder, until it finally warmed fairly rapidly to approx. current temps (the beginning of our current ~11,700 yr. old interglacial period.)
In other words, the flood occurred during what was already a vicious and long period of glaciation that almost did in humans — but also likely helped forge us. A brief warm spell likely triggered the flood, melting huge quantities of Canadian glaciers, but at present there simply isn’t enough ice in Canada (even in winter) to cause a repeat performance. I somewhat doubt that at present such an occurrence (a sudden release of huge quantities of fresh water) could similarly encore anywhere in the Northern Hemisphere, except maybe in Greenland — but I suspect Greenland would drain more gradually and “evenly”. Antarctica might be a different story, but I know of no evidence to support that. (Ok, I don’t claim to know “everything”!!!) :-)
The last drop in temps was indeed sudden and recent, and is called the Younger Dryas.
As you point out, the conditions have never become like the glaciation since those long-ago times, and nothing we can do would have such drastic impact.