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.

No experience with Somerset. We installed Homerwood natural solid hickory 6 years ago in a 4 inch plank. Our environment in summer is good with AC running most of the time. Winter is a different story, we heat mostly with wood & coal & do not run our whole house humidifier anymore, as it is a losing battle. I think humidity still stays above 35 percent, but not really sure. We have had zero problems with expanding & contracting. I don't know how much different a 1 inch wider plank would be, but our floor has performed well.

The answer is yes to Somerset in so far as "a good/reputable company." They've maintained operations for decades in Kentucky. Wood floors in kitchens regardless of the manufacturer will perform well. However, I am doubtful with the mainline fiber board core stuff that some use. "Surely ALL of the flooring manufacturers and their products can't be so terrible?" Step back and forget about it for a few days. Bad reviews come from bad customer experiences, lousy installer, or elevated expectations and most have nill to do with the manufacturer.

All wood has the ability to creak. It is the PREPARATION (levelling subfloor = extra cost = extra line added to the bill of sale) that allows the wood to sit FLAT. That's item number one. No, if you did not PAY for it, you do not 'expect' it to be given to you for free. Sigh...sucks but that's the way this cookie crumbles. To be clear, a concrete subfloor levelling job CAN COST $3-$5/sf to be done PROPERLY and would add 2 days or more to a job. Did that happen in your situation? Now onto the installation instructions: the INSTALLER (dude on his knees) did an INAPPROPRAITE installation technique. Any/all warranty is now void due to 'installation error' as it is called in the business. So...Here's where you are. You have a wood floor that was improperly installed. The question becomes, WHO did YOU PAY to have it installed? Did the FLOORING COMPANY include the price of installation with your purchase (ie. you used THEIR DUDE)? Or did you HIRE YOUR OWN installer (you purchase wood from company A and then had it installed by company B)? And JUST FOR sheeps and giggles, what is the HUMIDITY in your house right now? And do you have the ability to CONTROL the humidity with a push of a button (on your HVAC system)?