The biggest factor in preventing the grassy/vegetal aroma is contact time. I never, ever dry hop for longer than 5 days. That, in my experience, is the sweet spot for getting great flavor and aroma and preventing that grassy flavor. But again, my experience is almost entirely with pellet hops which have a higher contact surface area, so that sweet spot may be different for leaf. Maybe somebody else can comment on that.
Then how do you account for those of us who dry hop for months and don't get off flavors? I dry hop with both whole and pellet hops and don't get grassy flavors.
I have noticed that when I dryhop with higher alpha hops (Amarillo, Simcoe, CTZ, etc.), I get no veggie, grassiness, but I have seen this issue when I leave lower alpha hops like hallertauer or even Cascade in for over 5 or 6 weeks.