I don't see anything wrong with your idea as long as the lighter color stain is a complimentary shade that blends well with the flooring and everything else going on in the house.

You need to do a little more archeological digging still. You need to know the whole construction of the floor before you can decide how best to install something new. I'd take up that plywood piece in the kitchen and see what's under it. It's higher than the surrounding floor, so needs to go. You should also be able to see from there what subfloor is under the original kitchen hardwood. It's too bad the space under your entryway is finished, but I'd still do some exploring from below to see what's under there, and to figure out the fix to stop it from squeaking. Is it drywall below or a drop ceiling? I know it probably seems like a pain to tear out drywall, but if you cut out a clean patch, like 2' x the width of the joists, it'll be relatively simple to repair. Just make sure to cut it down the center of the joists so that there's room to screw the patch piece to it later. Cut the hole under the area that squeaks the most, if you can. Have someone walk on and watch the floor from below to see what's moving. It might be as simple as pounding in a couple shims from below, or face-nailing a loose board from above. You want to find out what's underneath the hardwood. It might be laid directly on the floor joists, or there might be 10" wide boards that the hardwood is nailed to. Another thought is to take out a board in the hallway, since that's not original and you want to replace it. See what the subfloor is there. I am a bit puzzled at why, when you've stripped the kitchen down to the original hardwood, it's still higher than the hallway floor. Is your current surface perhaps not the original kitchen hardwood? Peeling back the plywood area will help determine that. BTW, I haven't heard of that stop squeaking product you linked to, so can't offer any personal opinion. And don't pour self-leveling compound over top of hardwood. It needs to go over plywood.

From the images I found online it looks like an English Chestnut or red oak with multiple coats of poly on top

That's a foot print in the stain not just in the finish. Yes the 'fix' is to to a patch repair. They would sand down the area to raw wood, restain that area and then apply 2 coats of finish (with all the appropriate cure times to be observed). Then the entire floor gets a final coat of finish. It is the FINAL coat that offers the continuous finish/gloss level. To reduce your fears, Satin is a VERY forgiving finish. It has a lovely glow. This glow DULLS DOWN as it ages. It might start off as a HIGHER GLOSS Satin (be prepared) but it will ALWAYS settle down. This takes 1-3 months. So don't panic if you see a nice glowy floor on day 1. That will change. Once the 3 months has passed, the floor will sit happily at the satin level it was destined to be. Then, like all floors, it slowly dulls down withe wear. Higher traffic areas dull a little faster. So your foot print area (being in a high traffic spot) will mostly likely dull down nicely. The question becomes: Which bugs you more? A foot print such as the one you found (noticeable once you know it's there) or a *possible* sheen difference that will disappear with age? There is only one person who can answer that question - and that's you. Permanent foot print vs. 'disappearing' gloss difference? I'm not worried about the gloss level. I would worry about the stain variation.