If ** Electric Warrior** or anyone else reading has any spare time left, please give Meg Lee Chin a try.
Even if there was that one Pigface tour, I think she counts as obscure yet awesome.
Electric Warrior, let me know what you think of these two bands. I can recommend more like them if you’re interested in electronic instruments. There are a fair few electroclash and dance punk bands with female vocalists.
You left out my personal favorite: Jack Off Jill.
At the moment I’ll suggest The Kidney Thieves (industrial metal) and The Guano Apes (alternative metal).
Wow, that band is excellent, I’ve never heard of them before. Thanks for recommending them!
RE: the OP, Warpaint’s recorded material doesn’t sound anything like their live show to me (which just about ground me in the floor with their sound waves, it was so intense), but I think they are excellent. I don’t know if it’s what you’re looking for, but worth checking out.
The OP did specify “bass heavy,” though. 
Sleater-Kinney, one of my favorite bands, is an odd three-piece outfit in that they have two guitarists and a drummers–no bass.
I think some of Peaches most recent stuff might qualify. Or her from her last album. And here’s something more rocking from that same album. Her albums tend to be a mish-mash of musical styles, so it’s kind of hard to pin down. Sometimes, she’s shout-into-the-microphone punk, other times, electroclash, then a bit of glam or straight-up dance music. Quite an interesting artist, in my opinion.
The Dirty Epics, maybe?
I’ve listened to those bands before and I like them, but their vocals aren’t really in the style of what I was looking for. Still going through the replies - thanks everyone!
Pretty much anything by the Yeah Yeah Yeahs.
Their creepy video for Y Control.
Clouds.
Well, the OP specified alt rock.
Really? You’re using that song to represent L7? That’s bubblegum. Check these out.
The Intro Song to Natural Born Killers
Fast And Frightening
A little more on the heavy side, I present to you…
THE CYCLE SLUTS FROM HELL
I Wish You Were A Beer
By The Balls
Badass Mama
(Okay, I know they’re not what the OP specified, but it’s a loose definition. Besides, these chicks ROCK!!!
XX alternates between male and female vocals. Sometimes they’re bass-heavy, but often a single guitar line carries the whole melody. Give these a try:
