Well the HOST system gave me the itches unfortunately but others might find it works for them, I know one girl with hypersensitivity issues who it's ok for, so as usual it's an individual thing.
The sponge stuff looks like a cross between wet sand and the mushed up contents of an ancient foam pillow, it's slightly damp. I put an 18" patch down & it was brushed in with a stiff brush, looked like someone had thrown up unfortunately lol; took 6 hours to dry. If you had it in a whole room you could't go in that room til the stuff had dried out. Then you hoover it up. It has a slight fragrance if you put your nose near it. I'm sure it does the job, but I'm a little leery of anything which is going to take a while to offgass fragrance, however mild.
It's called a 'dry cleaner' but its really a 'damp-ish cleaner', might be good for those who need a dry cleaning system for their carpets.
I might re try at some point just to see how long it takes to offgass sufficiently so that I can tolerate it.

In the meantime - after a vast amount of googling I discovered this little trick for a VAX type carpet cleaner which won't take foamy liquids -

Use any detergent you can tolerate - dishwashing liquid/ laundry liquid - dilute as necessary & add a little of any fabric conditioner you can tolerate - the fab conditioner will instantly defoam the bubbles & you have your own home made carpet cleaning solution.

Spirit vinegar is recommended a lot (diluted of course) but I'd rather use something that doesn't smell like a fish n chip shop when you walk in a room. Also vinegar is very harsh - I wonder what that does to some carpets?

---

UPDATE - Ecover delicate laundry liquid worked a treat in our Vax for cleaning bedroom carpet - lot of dirt came up. Actually don't think the fabric conditioner is needed if you don't fill more than 1/3 full + empty the waste bucket when that has been used up - then refill as necy. The foam doesn't get high enough to shut off the engine in that case, at least not in ours. Tho adding fabric conditioner to the final rinse I guess might cut down on static and be a bit of a dirt repellant in any case. No reaction to any of this - usually I'm pretty bad with carpet shampoos.

though not an answer to the problem I have slept with hepa filter blowing on me [austin] .i slept far better ,woke feeling better . the fan blowing on you takes some getting used to ,and your partner might hate it .
shoot if carpet bothers you your mattress maybe also .