Warren,
Many good suggestions have already been made, especially concerning freshness and temperature. Of course, it's possible green tea is just not for you, but the world of greens is quite vast, and it's just possible you haven't found the one or several that appeal to you yet. I have lots to learn myself.
Some teas you mentioned trying are really rather distinctive (in my mind) such as the Japanese teas and pi lo chun. Japanese greens can be quite sharp in flavor and far "greener" (thinking of your mown grass analogy) than greens from China or elsewhere. I like them, but I can readily understand someone not going for them. Pi lo chun (in my limited tasting so far) is possessed of a specific basic flavor note which may not be for you.
Among the Chinese greens there is not only the vegetal -- you will discover the flowery ones (like Meng Ding yellow), resinous ones (like Shinya Yinzhen), austere and noble ones (really good dragon wells). And other taste parameters I'm not thinking of at the moment.
For "green" teas that may be more similar to what you already like:
In the puerh line, the Silver Needles Beencha (green puerh) available from Silk Road and IPOT is something you may find intriguing, as its flavors are rather bold and come from all over the spectrum, and yields a reddish brew. Same for some Yunnan greens I've had, which have more the intense character of many blacks.
And the couple of Bai Mu Dans I've tried seem to have leanings in the oolong direction. Though other drinkers may not get that the way I do.
Exploration seems to be the key. Buying from a good vendor is important. Getting a wide range of samples (from someone who packs fresh samples carefully) may be one way.
Joe