Can I root some suckers quickly that are are free of nematodes from a stricken plant, and reasonably expect to produce nematode-free plants if I do it in new sterile materials ... if no other diseases were a problem till the nematode explosion?

I love my plant and want part of her to live on!

leaves, more wilt by the hour,

What I think we are looking at are adventitious white roots budding out of the stem due to the plant's being nutrient sucked and root expansion/infection in a nematode explosion in the pot's soil, and severe galling there.

I received the plant as a gift and had no time for it, but it turned out to be the most interesting thing I had going this year by far.

The severe galling is apparent in the lighter green colored roots in the foreground, that's just a veneer of algae coloring the white sick roots that are exposed, from the eroded soil on top showing the legume-pod-shaped root nodules.

I am going to try to clone some of the healthiest suckers from the plant tomorrow morning, but the plant will probably be completely dried out by then. The vigorous aggressively growing plant completely crashed in two days, like someone threw a switch. This is because the pot was very restrictive for the roots, and the moment they galled out, it double whammy cut the supply and flow of nutrients and water to the stem in what seemed to be an instant. With 20/20 hindsight, though, it took about 5 days, but on day 4 hit critical. The adventitious roots were a wild attempt to access more oxygen.

That's my theory, anyway. The plant was a gift from a new acquaintance so I'm not sure if it was contaminated, or if contaminated soil blew in to infect the plant. All of his plants died by the end of June (sown as a group with mine), but that is considered the end of the growing season for many who aren't obsessive here

"The severe galling is apparent in the lighter green colored roots in the foreground, that's just a veneer of algae coloring the white sick roots that are exposed, from the eroded soil on top showing the legume-pod-shaped root nodules."

Ahh! That makes sense!

Florida can start a second season in August, right? Can't see why you wouldn't try with a rooted stem. When tomatoes are healthy, they have impressed me with their resilience. But DAAAAMN, when they are not, it seems hopeless.

I have a 1/2 acre in California, near the central valley, but have all but given up growing veg in the ground. Earthboxes have renewed my zeal.

Yes, it would be nice to start, inside, in July, so if these turn out disease free enough and like typical rooted suckers they are right on time. My zone is borderline Florida and challenging and frustrating as it goes back and forth. The Sun is somewhat better than San Diego for winter, but humid and more cloud cover, and vulnerable to arctic air which routinely reaches Georgia.

Unfortunately trees block my southern exposure during the key hours of midday in winter. They have the best conditions south of me, mid-state for winter sunshine.

Just finished scavenging 14 suckers and tips and put 12 in growing media and two in water for two I didn't have room for to watch anyway. They are somewhat dry and pale, but as you say resilient. The plant is now totally finished and the soil never dried out, if I'm thinking correctly about this, because the root system was shot and the humidity was probably being furnished by some breakdown duce to the nematodes and the fungi they host which are probably some of the unmentionables.

Anyway, the reason I am worried about trying to root them is once the nematodes start, I don't know whether the pathogens they carry would have gone systemic in the plant and it already be too late. I guess I'll find out. I really hate the prospect of potentially culturing sick plants though because in the house I just don't want to be spreading those sorts of spores around (or an errant nematode spawn that magically appears high up on the plant). Because then I'll be concerned about my seedlings getting sick.

I feel so sorry for my plant, the first time I ever named one (Charlie Buckets, a girl LOL) to have lost its last leg and then be butchered by me on its remaining growing tips. It is interesting to see how the plant protected the growing them to the end by somehow transporting nutrients from all the other leaves selectively to them as it crashed in a short time even though the root system wasn't furnishing the pressure from below. That's why I quoted and completely agree with your sentiment!

Good luck with the Earth Boxes, they are fabulous systems and I've made some generic models. The soil here is hopeless. Also the tomatoes are always greener on the other side of the state line, or so I think.