> I used https://github.com/azimuth-project/el-nino/blob/master/R/grj/nino34-anoms.txt

Did you use https://raw.githubusercontent.com/johncarlosbaez/el-nino/master/R/average-link-strength-1948-2013.txt at all ?
I am wondering if that data is the same in your work, Ludescher and my analyses.