"Any idea what a mechanism linking earth's magnetism and climate might be?"
When you want to go to Florida in the Winter, you end up in Canada 'cuz your compass is all messed up.
I'm not real sure what the big deal with the magnetic reversal would be. I think the one thing is they don't know if the field weakens as it revearses, and how long the reversal process takes. The magnetic field protects us from solar radiation. No field and things would warm up pretty quick and dramatically.
Now if we could get enough tinfoil ........
I don't think the mag field goes to zero. It's not that uniform. It develops swirls and eddies and the poles move around wildly, sometimes there are two north poles. No kidding.