Your OUT in your iPython notebook in #39 here clearly shows a lump not a linear dependency between the link and anom.
However in you ANOVA analysis in #41 you are using lm simple linear link~anom which is fully linear regression.
Let me know if I am misunderstanding something. I generally and easily misguide myself with ANOVA, so please have that consideration.
Support Vector Regression (SVR) does what you are trying to do here (if I understand it correctly) but in the non-linear or curved space, it uses the kernel and maps, non-linearly, into a linear space and does then linear regression and then maps back non-linearly and produces a non-linear regression. I attached the math in my SVR forecast.
Thank you for this work, I know how much hard effort it is.