I've brewed hundreds of dryhopped American IPAs and IIPAs. The longest period I dryhopped was only 14 days. I usually hover around a median of 8-12 days, and found no benefit of a lesser 3-5 day dryhop by comparison. I have used both pellets and leaf hops. Dryhop temps. are typically 64-72 F. I've done it in both the primary and secondary. And I have never experienced a grassy, vegetal, green character from these beers.
With that said, I tend to primarily use American, high alpha, Pacific Northwest hops like Citra, Amarillo, Simcoe, Centennial, Chinook, Horizon, Columbus, Apollo, Nugget, Summit, etc. - These beers are always either quite fruity, citrusy, tropical, dank, resiny, floral, or all/some of the above.
However, perhaps you could get some of that vegetalness by dryhopping for an extended period with a hop that isn't necessarily great for dryhopping with like Perle, Magnum, or any of the other Noble, European varietals. I never bother with these hops late in the boil for my IPAs.