I don't think it's practical to replace the staircase - too costly. I agree, I would try to stain it similar color.
For what it's worth, very often, the steps are a different species and/or grade of wood. For example, in our area of the country (northeast), you will often find oak floors and pine steps.
Also, if you the color/graining difference bothers you, I would recommend adding a carpet runner on the steps. In fact, I would recommend that regardless from a safety and design perspective.
You might find this article on carpet runners helpful.
http://theflooringgirl.com/blog/carpet-runners-for-westchester-county.htmlDebbie Gartner, The Flooring Girl