Although as you've mentioned in your most recent response, the hill dwarves could have gathered the "improved" soil from the mountainhome. That's my headcanon for now, at least.
How would that work anyway, if you were to add a soil gathering zone? Since soil is a material and is the same regardless of depth, plus cavern floors are currently just rock overlaid with mud. Would the rock/mud gathered from a cavern have a special flag for plot improvement use?
Perhaps we'll discover pigs and poultry will convert muddied stone into cavern floors. Pigs in particular were iron age cultivator's champions, widely used to clear small plots for horticulture. They'll uproot and "plow" a plot of woodland, clearing tangled briars, digging up rocks, toppling saplings, and small trees, preparing the soil while providing fertilization and soil aeration. Irish small tenants and cottiers were still using the method in the 19th and into the 20th century. They'd finish digging what they reasonably could of potatoes and other edible roots, then turn the pigs into last years plot, and plant the pig's old yard. Poultry will clean up a lot of what pigs miss.
I can imagine dwarves moving livestock from plot to plot like this, and pigs sure do like mushrooms! Perhaps some cavern beasties could be assigned a plowing flag as well, drunians look like they might enjoy a good root while watching for easier food to steal, and I could imagine draltha doing it without really intending to!
It would be a clever way to use animal fertilizer without dealing with fertilizer products.
Another "new farming" question: How does a potash fertilized muddied stone/soil plot compare with cavern plots? How about with potash fertilized cavern plots? Some cleverness with the numbers could make potash fertilization useful for more than specialist early quarry bush cultivation.(clinodev spent much of his childhood bewailing the fate that put him on a farm, and half of his adulthood kind of wishing he could go back. So it goes.)