> The project-based track will require a larger time commitment
This is the only part I take issue with. I tried a take home interview once that took the better part of a weekend and decided I'd never do it again. There just isn't enough time. Basically, if it takes that long, there needs to be a very high chance that I'm getting hired at the end, or it's not worth it.
On a hash with a million elements, the O(n) hashing of a 10-char key is negligible.
Also, you have to make apples to apples comparisons. In this case, you're comparing the time to search against the number of elements, and that's it. If you want the time to hash AND search - as a function of n - then your analysis holds, but you can't then compare that against other datastructures that do not have an equivalent hash step.