Greetings!
Well, Joshua, I suppose you could assign the following:
STR +4
DEX +0
CON +2
INT -2
WIS +0
CHA -2
This could provide more of what you are looking to acheive.
On a tangental matter, I will admit that my approach to making races (among other things,) is the first priority to me is realism/faithfulness to the concept, and *balance* is distinctly secondary. Not that balance isn't important, mind you, but that I find it more important to remain faithful to the creative concept, than what some might engage in as a slavish kind of adherence to *balance* For example, if you were to adhere strictly to all of the *balancing* strictures in the DMG in order to make your race, you may indeed have a race that is no more, and no less desirable than a standard human, but in the process you may have diluted your original concept to a point of minimum returns. Do you see what I'm saying? Not that you are a slave to *balance* per se, it's simply a concept that while important, can also infringe on your creative processes. If your race is somewhat "unbalanced"--I say "so what!" Then again, I perhaps have the luxury to say that because I have players that almost without exception design their characters from the standpoint of "concept" rather than any mechanical considerations.
For example, in one of my campaigns, I have one player that has selected to play a Minotaur Wizard. Minotaurs, in comparisson to humans, elves, or others, make decidedly poor Wizards, and yet, the player simply likes the thought of playing a Minotaur who tries to master Wizardry. The fact that Minotaurs have a number of difficulties in being Wizards doesn't bother him at all.
In your Neanderthal example, if the Neanderthal is somewhat stronger and so on than a normal human, besides stats, there are other things that you can do to *balance* them. For example, you could not apply the (+1 Skill Point) per level that normal humans get; You could strip the Neanderthal of a initial bonus human feat; You could make the Neanderthals illiterate; You could even restrict what classes that they can be; for example, no Clerics, because Neanderthal religion isn't of an organized type; No Wizards, because the Neanderthals simply don't have a concept or tradition of Wizards; No Paladins, because neanderthals don't have the cultural concept or the religious sophistication and organization to give rise to Paladins; These could help.
In another thought, you could apply a (-4) to INT to not so much reflect that Neanderthals are stupid, but to reflect the fact that they adapt to new knowledge and ideas more slowly. I also apply the different bonuses and minuses to stats to meaning different things--which the rationale behind doing so is not always the way that many people think of it. Do you see?

I hope I've made sense!
What do you think?
Semper Fidelis,
SHARK