There are two possibilities:
1) all things are only accidentally so in our world (including triangles, according to you). In which case, we will never have enough information to say if the sum of accidents is "better" or "worse" than the sum of accidents in any other world. The only "proof" of such a world would be experiencing it, in which case it wouldn't be an "other world," it would be our world.
2) some things are "necessarily so," in our world, in which case they would be necessarily so in all worlds we can possibly "image-ine," (that is, conceptualize).
Thus with respect to pain, the "bad-ness" of pain either follows from its definition, or it doesn't. If it follows from its definition, then there is no possible world in which pain will be "good." If it does not follow from its definition, then pain need not be bad in this world either.
edit: this is why I said Leibniz's theodicy is "nearly apodictic": his argument is essentially deductive, flowing from the very nature of reason and experience. Now, whether or not this constitutes an acceptable theodicy is a different question entirely. My point is that anybody can see the unacceptability of the argument; it takes a philosopher to see the cleverness of the argument.
On the triangle. It differs from pain because the sensation of pain is real, while the triangle is a concept we use to simplify the actual world we interact with. There are no two dimensional objects that I am aware of, and changing it to a pyramid still runs into the problem of needing continuous mass in that shape. A four sided triangle may be impossible, but at the same time a three sided triangle seems impossible and we accept it.
The world that I'm imagining where it is this world except pain is something different is a new world.