Lighting a green screen is even harder than lighting a whiteboard. And performing in front of a green screen also requires practice different than that of writing on a whiteboard.
Here are two alternative strategies which you can possibly blend to taste. The first, and most obvious, is to get a standard 4'x8' bead board. Put that board on the wall opposite the white board. Aim a focused, bright light to fill the 4'x8' bead board. This will send diffuse light back to the talent and the whiteboard without a specular reflection. If you need to, you can cheat the bead board to one side or the other so that you don't have a "warm spot" (a very large, diffuse hot-spot) in your whiteboard. For illumination, start by looking at this ARRI 750W flood and then adjust to your favorite illumination source (LED, HMI, plasma, CFL, etc). But don't lose focus and barn-door modifiers. You can also raise the bead board off the floor to span the angle between the rear wall and the ceiling. You can also place the bead board on the rear ceiling and bounce the lights toward the talent from on high. The shadows, etc., will tell you how high the bead board needs to be to make everything look right.
The second strategy is to stay with the idea of a pair of side lights, but get a pair of tall vertical light baffles that you can use to completely shade the whiteboard from the lights. Ideally the shadow pattern is such that the whiteboard itself is shaded from the lights but the talent in front of the whiteboard is not shaded. Because white is so bright, you actually don't need a ton of light on the whiteboard itself--it will look white when the ambient (ceiling) light hits it. But you do need light on the talent--skin tones are several stops darker than whiteboard white. So let your side lights hit the talent and not the whiteboard.
It should be obvious you can combine these two ideas. Beware of mixing color temperatures (i.e., don't use daylight CFLs for side lights and tungsten lights for the bounce board or things will look weird).
