PTR_K

I can think of three options, none are perfect, but each could be tinkered with to get what you want:

In the Light of a Ghost Star – This is much further in the future than you intend. But it has incredibly simple rules which are easy to customize. Also I made a psionics supplement for it here. I had pretty good success running it.

Mutants & Machine-guns - A loose, fairly tongue-in-cheek system. Free.

Mutant Future - Basically a cleaned up clone of early edition Gamma World. Less light than other games mentioned.

Huh. Tried posting this response before, but Jerbo apparently ate my post.

I frickin love GURPS Ice Age supplement. But never have run it for two reasons:

1. After years of consideration I've come to the conclusion that I just don't particularly like GURPS as a system.
2. I can never think of stone age scenarios that feel compelling in my mind. Not sure what quality would quite seem satisfying.

But still have some fascination with a dawn of humanity type setting.