If the stand is small, your fingers are the predator. If the stand is big, chop it. The size of the stalk near the end of it's life (september) is not really important for the size of the tuber. The tuber has more or less reached maturity. And they just re-grow stalk and leaves as needed. Since you're not eating the leaves, you could probably just let the nibblers eat. It's much more of a problem on brassicas when you are eating the leaves so they need protection.
Birds are probably a predator, but I'm guessing you haven't researched which birds eat those things and planted the right plants to attract those birds. That would be a long-term solution.
Do you have something you can
feed them to? That might be worth the effort of picking them off.
Another option is finding out what that animal REALLY likes to eat and planting a catch crop. You're currently feeding it apples but you could be growing ice-cream for it, which would divert them away from your sunchokes.
William