While I haven't downloaded the mod, there's something I'd like to comment on:
This would be okay except for the fact that at +4/+4/-4/-4 they give me a net 0 gain.
A rule of thumb I learned long ago is that a penalty is usually worth half as much as a bonus, because you'll only do something when you really need its bonus and/or don't care about its penalty so much. That is, your personal utility function isn't flat; you'll value one point of X more than one point of Y in a given situation, while that might reverse in a different situation. (Smart players can take this even further, completely removing the negative impacts while maximizing the positive.)
Maybe your city is at a comfortable size (ICS?) and you don't want Food any more. Anyone who's turned on the "prevent city growth" option can see the point here.
Maybe you have the policies you really wanted and aren't hurt by a culture penalty. (If you've just gone on a conquering spree, you'll never get enough culture to gain lots of SPs, so why bother trying?)
Maybe you've built everything you need to in a late-game city and all you have left are Research, Wealth, or churning out units you don't need; in that case, you don't really need production. The 25% conversion rate means a -4 production only would translate to -1 in gold or research.
Maybe you've reached Future Tech and don't need any more research. All it adds is score, and who really cares about that? You don't even need to wait for Future Tech for this one; if you've just unlocked Tanks and know that one good military push will win the game for you, kill your research and put everything into production and gold. That's what we did in Civ4...
That sort of thing. So, a +4/-4 is basically balanced with a +2/+0 in practice, as long as the players/AIs handle them intelligently, because the player will use the +4 that helps them the most in the current situation while hoping for the -4 to be in something with the least impact. Of course, in the case of Civ5 the AI will have no idea how to use your specialist, and is likely to end up allocating several specialists that exactly cancel each other out. So that just won't work well either.
But that math note leads to my first criticism: +4/+4/-4/-4 is WAY too much for a single citizen. It's just too big a swing; it sounds like you're trying to mimic Civ4's sliders in effect, but this sort of thing leads to a bad strategy I'd seen in several other games: if the impact of the "flexible" part of a system is too large, then that becomes the ONLY way to get things done. In Civ4 you'd get this to where people would shift the sliders to "science mode", "money mode", etc., with very little in-between. The only time I'd ever use the Culture slider was when I absolutely HAD to. I see this happening the same way: if you make specialists that add significantly to, say, production, then a city trying to produce a critical Wonder will use as many of those as it can, and the difference between that and a more "normal" strategy will be so large as to make the latter untenable.
It's similar to how tiles work, in that you'll work your mines and such when you really need to build something fast, but the difference isn't nearly this large. The difference between working a non-resource Mine and working a Trading Post is only 1-2 points either way, whereas you're proposing a shift of 8 (going from a +production specialist to a -production one).
This is especially bad since Civ5 is built on the concept of multipliers; the base values for production, gold, and especially research are very low, but you've got stacked +50% buildings to improve those. So if your specialists add +4 to base research, it might actually be more like +12 beakers added in the end. And this ties back to the previous points; while on paper -4 culture balances +4 research, the -4 will stay -4 (unless you have a Broadcast Tower or Hermitage, which are VERY rare and late in the game) while the +4 will be more like +12 from the University, Public School, and Research Lab. So what might be balanced in an early era becomes completely unbalanced in developed cities, especially if you specialize the cities; if you know city X is going to be running a bunch of -research specialists, then building Universities and such becomes a BAD idea.
So I'd say drop them to +2/+2/-1/-1, which addresses all of the issues I'd mentioned above: its absolute net is +2 (so a stupid AI won't accidentally cancel itself out), its "effective" net is +3 (still reasonable for a good player and comparable to the yield from a tile), and the per-specialist shift is only 3 points at most. The numbers are small enough that even with multipliers it's not really a large enough shift to throw the balance way off (again, comparable to tile yields).