also, drawing more (but smaller) pieces seems slower to me.
That seems surprising. My experience is that graphics cards of the GeForce 2 era work well with 256x256 size textures or thereabouts, but performance drops dramatically with anything much larger.
If I break up the board I can't see them fitting back together correctly because it's a perspective view.
Do you mean that you use SetRotation before drawing the board? If the board graphic itself is drawn with a perspective view that isn't a problem. Is the perspective changeable?