John, I think in the end you're going to have to buy some yellow pine board comparable to your tread material, and just do some sampling, which is the point we all eventually come to. There's no pat answer when it comes to staining, especially matching different woods, even two different pieces of the same wood, even from the same tree. And doing it through pics is not going to work.
Fortunately, you're not looking at a huge color difference here. I still say the handrail only has a clear coat. I've never seen a new construction job where handrails were anything but just clear coated, but all areas are different. Remember, even if you get the color right, you're not going to mask the difference in the grains, even though I missed it initially. :laughing:
Personally, I still think this is a better question for the flooring forum. While painters do stain, hardwood flooring guys do a lot more, and I can imagine this would be a more routine question for them. Or, hire a floor guy to do it for you.
Or, you could hire a carpenter to install oak tread and riser overlays. I've done two jobs in the last year where they did that, and I just came in and clear coated them.
What you do depends on your patience, and your handiness.