This is a request for a sort of twist/inversion of NTR (I don't think I posted this before): the "hero" is the one who takes the girl from someone else, but that someone else is a total bastard who doesn't deserve the girl. Not that the guy who "takes" her is necessarily better, but still.

Best example I can think of off the top of my head is NTR Shoujo by NAGARE Ippon. The MC is the obese assistant of a manga artist. The artist's niece adores him and is secretly sexually involved with him. The assistant has adored the girl for some time, and has grown to realize that his boss is just using him for his talent. His boss even steals his work with promises to put a good word in while telling the editors that he doesn't even HAVE an assistant, doing everything he can to make sure that the MC is trapped as his assistant from here on, unable to move forward and watching as his boss is praised for his work. You still feel bad for the girl being taken and broken by a guy she'd never considered as anything more than a nice acquaintance, but still can't help but feel the boss doesn't deserve her and maybe find it ironic when she cries out for such a bastard.

This act of an underdog taking from a bad guy is plenty for me, but if possible I'd also like to see if there are any where the underdog doesn't "break" the girl or convince her to accept him through sex, but rather reveals to her what sort of person her beloved really is and changes her heart in that way.

You can try Love Distortion (YOSHIURA Kazuya) by YOSHIURA Kazuya
It's a mix of different type.
Carefull some are good NTR (chapters "Friends" and "First Love Compass"), so you'll probably hate them. But the last chapter, "First Time", should be what you want, and the chapter "Little Problem" could be something similar (except that the main guy stole the girl for a funny reason)
Anyway the art is damn good so I only can advise you to read the whole book... xD

I thought when it's stealing from the bad guy, it's called netori.

Indeed. Those are two different tenses of the same word. Taking a girl = netori, having a girl taken from you = netorare. I'm just looking for netori with a minor stipulation that the guy being taken from is a bad dude. Doesn't even matter if the guy doing the taking isn't much better (for instance NTR Shoujo's MC doesn't exactly come across as a "good" guy even if you can understand his vengeful motivation).

Another good example if I understood the content right is Nekogen's Namahame Debut. The young main character isn't winning any prizes for kindness, but the guy he goes against is really messed up. If I understand it right the guy pretty much controls his school and dictates for certain people to be bullied and persecuted and others manipulated, all while grabbing every girl he wants up to and including classmates' baby sisters. The MC then comes and literally steals every last one of them and plays videos of all of it while stealing his fiancé live in front of him. Again, the MC's not really what you'd call sympathetic but you still want to see the downfall of a villain who's hurt so many and viewed everyone as nothing but trash.