Which languages have changed the most drastically in the last 1000 years?

When Bergsland and Vogt (1962) debunked the assumption in Glottochronology that core vocabulary is lost at a constant rate among languages [Bergsland, Knut; & Vogt, Hans. (1962). On the validity of glottochronology. Current Anthropology, 3, 115–153], the lexically conservative language they brought up was Icelandic.

The lexically innovative language they brought up was Inuit, which has taboo replacement of words. (If a word has been used as the name of someone recently deceased, or even sounds like it, you get rid of it. It might come back in a couple of generations, if anyone remembers it.) Australian indigenous languages do the same. Such languages may well be stable grammatically, but their vocabulary undergoes a huge amount of churn.