I have a 4 acre field that has seeded itself over the last few years. If I were to mow it, then plow it, leave the roots to dry for a day or two, then harvest would that qualify as an appropriate method to harvest the roots. Are there any tests that would need to be performed to tell if they are the appropriate quality? I have heavy clay soils, and it could be difficult to get all the soil off without some form of washing.
Yes, that would be one way to start the drying process. But, I would pick the root up at 40% moisture (usually only one day in hard sun), and then rack-dry the root to 12%. Later roasting the root at higher temperatures causes the various flavors top set differently - when used as a coffee substitute.
Most sources for Dandelion root only field-dry the root, holding labor costs down. Shade and air-drying techniques will significantly change the flavor and way the root is roasted. Just like coffee-beans, this part of harvest can make a significant change with who can use the root, and for what cottage industries (application).
Most don't know that your mouth (and eyes) can be trained to be a "laboratory," to sense variations in when and how to cut and harvest a crop. Determining when to pull rootstock for "best flavor" can take years to learn (from experience). Or you can have test plots, where you do several different forms of harvest.
So, whenever you grow crops like this, use your mouth and eyes - to taste, smell, and examine various changes, from to harvest post-harvest protocols. The way you choose to "set a field" for next year's crop is also important. How you plow might also set the field differently. And, you might even be able to enhance further and higher yields.
Heavy soils can be easily changed, over a three-year (green manure) program. Mychorhizzae can shorten and enhance those programs. Washing the root (on concrete) is a given. Normal film, found on the outer root, should not be more than 2%. There are many easy ways to clean the root in post-harvest protocols.