It will be obvious simply because the new wood will be tight and have little to no gaps and the old will show obvious gaps.

Color will be a little off but even a light stain with just a little color will help hide that difference.

When you look at the proposed idea the first thing you will notice is the gap difference.

Could prestain the edges of the boards black so as to match the old; instant dark seams.
2 yrs ago they were selling prefinished flooring with this effect; they called it French Bleed or something?
Casey

Thanks, gregmills, I hadn't thought about expansion/contraction. We're going to suck it up and spend the extra cash even though we'll be trashing a perfectly fine floor. At least it's not a large area.

Thanks, Sombreuil, for the suggestions, but we want the oak to come close to matching throughout the house, so plain old white oak is what we're committed to (so at least we can keep 70% of the flooring in the house and just refinish it).

You've made a reasonable decision.

Almost exact matches can be done, but the skill and knowledge level has to be high for success. Time is expended identifying characteristics of the existing and finding new material that will work. Also, weaving in the new with the old is labor-intensive, so that also adds to the final cost. Then there is the finishing itself that needs adjustment to make it all look correct.