Perhaps the best response to the commandment involves a combination of our suggestions: discipline which results in reshaping habits of the heart/mind; shutting down covetous thoughts as soon as we detect them; defusing such thoughts by observing them in a detached manner. When it comes to handling dangerous matters, I tend to favor having more than one option.
I remember your fondness for Jean-Yve LeLoup's suggestion ("you can" rather than "you shall."). After reflection I find myself in disagreement, assuming I understand what is being said. I'm not at all certain that "we can" fully actualize any of the commandments. On the other hand, observing them as best we can will change us. In terms of the commandments, such a change involves becoming ever more devoted to God and more respectful of community-building boundaries.
Personally, I sometimes think of the commandments, including "You shall not covet," in mathematical terms, specifically infinity. We can never reach the end of the matter, but each improvement in its approximation is good in itself. Shifting to an analogy from physics, knowing we can not achieve the speed of the light does not negate the potential value of getting ever closer to it.
From my perspective, the commandments may also serve as needed reminders of our limits. The very fact that we cannot fully implement them introduces us to the complexity of our natures, including the tension between the image of God within us and what one might call our shadow side. The image of God within us is drawn to the commandments, wants to embrace and practice them, knows they represent in part what it means to be fully and healthly human. Something else in us, though, fears and hates the comandments. This shadow-self sees in them its potential demise, whether through elimination or transformation. And it fights back. With reference to the prohibition against coveting, it tries to dull our senses, so that fail we to notice our thoughts and feelings and the way they affect what we do. Sometimes it turns very bold and challenges the commandment itself, asserting, "Greed is good" (to borrow a line from a medicore movie).
When we pay attention to this kind of thing, we may get in touch with our own sinfulness, that is with the way we consistently fall "short of the mark." Such self-awareness may push us in any of several directions: trying harder, giving up, humble acceptance of our limits without ceasing to try, a growing awareness of God's grace which frees us to go on trying in the same sense as chldren undertake difficult tasks without fear their parent will cease to love them should they fail, and the like. Each of these possiblities, plus others we might imagine, requires more space than this post permits.