If there were only 3 or 4 types of bonuses instead of the 10 or so there are now, I think you could reduce the problem without breaking the math.
This. No more than 5, tops--and only that many if you need that much to really make everything clear and easy to use.
If you want to retro fit or otherwise deal with the possibility that you might not have a complete handle on it (new edition), put in some diminishing returns. That is, you might have a chart where everything up to +5 in bonuses counted as +1 each. But getting to +10 in bonuses only bought you +8 total. That is, you assume that there was some non-stacking stuff inside that category, but you don't worry about what exactly.
However, that is a bit fiddly, even for something like 3E or 4E. So an alternative that is almost as good is to simply put in a cap, that moves with level. Make it high enough that the only way to hit it is to power game fairly heavily or go nuts in one or two categories to the neglect of the others--but not quite so high that it is impossible to hit. Now, it doesn't matter what combinations people come up with, there is a max limit on what you can get. Or if you want people to be free within categories, simply put the limit on the total, after stacking.
Now, power gaming shifts from breaking the math via inflated chances to hit to efficiency of getting to the cap. While this can still be a problem in some games, it has limited payback if the rest of the group is in the ballpark. If you can get to the cap more efficiently, saving yourself 2 feats compared to the guy next to you, what are you going to do with the two feats? You can try to power game some other element, and I guess some people would. But if those weren't your first choices, you are already being restrained. And at some point, even the most stickler of power gamers says, "Heck, chuck it. I'm not killing myself for another +1.375% increase in effectiveness. Linguist is looking fun for this guy... "
BTW, this isn't just limited to handling runaway effectiveness, either. With a cap, you can also put in a floor. Then you shift from, "take what sounds interesting or take what makes you powerful," to, "get numbers in this range somehow that interests you, and then take interesting stuff from there on." The best thing about that is that a cap and floor, being essentially assumptions about campaign style and the degree of balance needed, can be tweaked. The designers are telling you where people should be to fit what they designed. If you want to go outside those boundaries and let people be disparate in combat effectiveness, you can. Just widen the range. If you widen it a little, you know you or the players might need to address an occasional issue. If you widen a lot, you know the group is taking responsibility for this aspect (to the extent that you even care).