Cryoconcentration, can you do it yourself?
Yes, you can do it yourself:
People have done this to concentrate alcohol, and other water contaminants, at least as far back as the middle ages. Example: 


  Fractional freezing -- "jacking" in old parlance -- has a long history in the United States. The beverage applejack was produced using this method by first fermenting apple juice into hard apple cider. Then barrels of this cider were left outside during the winter and the connoisseur would occasionally fish out the frozen chunks of water, leaving an ever-concentrated batch of hard alcohol behind. At some point in the 20-25 percent ABV range, the liquor would stop freezing at ambient temperatures and the booze was ready to consume as "Jersey Lightning." It was also used as currency.


Wikipedia has a short piece on fractional freezing, but you're better off looking into use by home brewers; ignoring the alcohol part of the equation of course.
Generally stirring is not required. You just let the liquid partially freeze, then pull out the ice chunks. The result is relatively pure water ice, and concentrated juice of whatever you started with. Obviously, you can repeat the process several times to end up with a stronger juice. As the phase diagram in link 1 shows, a -20° (-4°F) will get you alcohol up to 30%.
Bear in mind that the fractionation isn't perfect, and some compounds tend to freeze along with the ice more than others.

The existence of Applejack suggests that your apple juice concentration scheme will work. I'd just not bother with the stirplate.