Karima Amos

I also agree with the sand plan. I till the upper few inches of soil with a hoe (small garden) and I also break with a turning fork so the roots will grow deeper. Seeds go about a half inch deep and every couple of inches, I put a radish seed. Daily water (or more often during hot dry days) until everything's established. The radishes germinate quickly so I know exactly where the row is.
I recommend starting with 'Little Finger' carrots. They are delicious and don't need deeper breaking. 'Parisienne' as suggested above is even a better idea. they also mature more quickly.

Takes time, but I'd air layer that beauty.

Make enough of a vertical cut in the lovely winding basal stem to pierce the woody outside layer. If you have rooting hormone powder, apply some (if not, it will be fine). Pack a couple of handfuls of wet horticultural moss (the kind used for orchids) around the cut place, and wrap it all with something like plastic wrap, securing with string or twist ties. Roots will grow from the cut, and when they're big enough, cut the original roots away.

You can do it all without moving the plant. This will still mean a top heavy plant, though.

I, too, am finding this problem, and I'm also in 6a.  I know there's a late blight that affects tomatoes in this soil, so the mention of- was it fusarium- rings true.  My colony of sunchokes is elevated but the past two weeks have been very wet following a droughty August and September.  

My chokes did get a fungal disease several years back, and the supplier at Ronniger's (yes, so long ago that it was still Ronniger's) talked me through a treatment that got rid of it.  It was a drier rot than this and showed earlier, including a wilt. That disease hasn't shown in many years.

I have long dug them through the winter, at times when the soil thaws, because all storage I've tried so far allows them to rot, and I can't use up the huge yield before they go bad. My location's winters have gotten much milder over the past decades and it's unusual for the soil to stay frozen for long.

Here's a question I've got, though:  I have been intending to send a start to my friend in Sacramento, but I'm wondering if I should not do this, or if I should send anyway and advise her to take it to the local ag extension office before putting them out.  Many tubers are not visibly affected, and, of course, I'd send her some of those.  

Thanks.