DA:

"When we talk about abrupt changes ... the last one of record resulted in quick-frozen Mammoths in Siberia. And that was quite a bit longer ago than 300-400 years."

An explanation I read years ago about frozen mammoths suggestd they had been trapped in avalanches, fallen into snow drifts or through ice into bogs or lakes. No need to postulate rapid changes in climate. As you say though even 300-400 years is hardly really rapid.