The article Woodmorappe references does indeed show a lot of variation in C14 , but in trying to refute Lake S.'s data, what he omits is telling.
The study is on a speleothem, and there is very good agreement with LS out into the 30.000s, with of course their basic agreement with C14 measurements. It is only into the 40,000s that there are some wild swings of C14 shown. They also show agreements into the 30s with other studies - Lake Nisan, Cango cave, and 4 others.
So his reference is providing evidence against his case - I guess a depressingly common thing at ICR.