How does washout affect the wing incidence required?
That depends on the taper ratio.

In the end, the wing with washout should produce the same lift as the one without. For a rectangular wing and 2° washout, your reasoning is right and the root should have 1° incidence so the whole wing produces the same lift as the one without washout and 0° at the root. If the wing has a triangular planform, however, the tip contribution to overall lift is much lower and the root incidence should only be 0.667°.

For a general rule, pick the position along the span at which half of the wing area is inboard of this position and pick the root incidence such that the local incidence at this position is 0°.