IMO Shinzon wanting to wipe out Picard and humanity because they lived such privalaged lives while he suffered endlessly, and because he's a copy of a great man and would never fit in there, was believable. It didn't make rational sense, but it wasn't meant to.
I don't think he was supposed to be insane. If he was, it kind of ruins the whole "dark mirror" angle of the character, as if he's genuinely crazy, his motives and actions aren't going to be rational or worth much analysis.
I agree that is crossing the line to making an excuse for the film - in real ife sometimes people do random irrational things because they go nuts, killing your wife's lover in a fit of passion for example.
Spending years on a plan is not the work of a crazy person though, there is motivation. Hitler really genuinely believed all the stuff he spouted about Jews, Untermensch and so on, and lots of people still believe it all. He was a mass murdering evil bastard but he HAD motivation. The same goes for the 9/11 attacks, the attackers were not crazy, they HAD motivation for what they did.
So shinzon could easily have been written as an evil murdering bastard, which is just fine, but he needed a motivation for his actions explained on-screen to the viewer.
I actually quite like Nemesis, but the script needed some re-writes to better develop what could have been a very interesting villain. It doesn't take much, look at Khan for example, motivation for revenge on Kirk.. "they killed lots of my friends, and my wife, because that bastard Kirk left me here.." no problem!
The closest you get in NEM is Shinzon's line "the victory of the echo over the voice" where he seems to be positing that he is showing his superiority to Picard by destroying everything he cares about. I don't believe it though, RE-WRITES NEEDED!