"Stock-like" Android (JB+) ROM for unlocked i9300
I've been looking into rooting and flashing my i9300 for a while now. I've basically tried to revert TouchWiz back to stock Android by installing mods from the official Play Store, but it doesn't quite cut it.
I just want Android. I don't want what Samsung thinks Android should be.
I've read the sticky here, but all of the listed ROMs are TouchWiz. Is there any way to get an Android "stock-like" ROM on my S3? Preferably a stable version, JellyBean 4.1.1 or above.
From what I've read, I need a modem, kernel and ROM - is this correct?
In an ideal world, my S3 would look like an over-sized Nexus. I don't care for multi-screen (who does that on a phone?), or "slide to phone". I know I'm somewhat belittling TouchWiz, but it really does seem unnecessary to me personally.
Thanks in advance for any advice. I've posted this here rather than at XDA to prevent any nerds getting their e-peen out for my simple questions.
Samsung S3 i9300; Illusion ROM (4.2.2)