How should I store sunchokes for 4 months in a hard freeze? I've seen that sunchokes "just want to grow", so I was wondering how I should store them over a long cold winter.

This is mostly so I can have seed (community garden) in the spring, but I will also be eating some.
Keep them moist and sealed in a bag at around 32F. Treat them a bit like potatoes except that they are resilient to frost and freezing. In fact, they do survive buried in frozen ground over winter.