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.

Quiet walk's vapor barrier is designed to seal around the nails or staples, when shot through. The heat melts it in place. The built in vapor barrier disperses the vapor to the perimeters. The 1/2" gap left at the perimeters allow the moisture vapor to escape. I believe the perm rating on it is .7 , which is below recommended rating. But the product is approved for wood floor use. NWFA had a course on their products. You cannot use quiet walk on subfloor that measures above 7lbs of vapor pressure. It needs to be dry. Aquabar allows vapor to go through the material at a slow rate, but deflects most of it to the sides and up the walls. If, your crawl space is less than 18" high. You need to get it weather wrapped before starting the installation.

Thanks for bringing me back into the discussion. First things first: you NEVER use carpet underpad under anything but carpet. EVER. So now that is out of the way, we'll move on. The QuietWalk Plus is allowed to be nailed into. Very good. So too is the MPGlobal. Excellent. We are officially working with Apples to Apples. Nice. Now onto ACOUSTIC RATINGS.....shise (German...allows me to swear without getting flagged!). You are now into a WHOLE NEW INDUSTRY of trickery and crap...with some crapola on the side. And a desert of kaka pie! Nope not kidding. This is one of the LEAST understood parts of the building industry. And the underlayment manufacturers LIKE it that way....which is why they spend big bucks lobbying to KEEP the industry 'stupid'. OK. That's my rant. Done. Onto SCIENCE (yah...big cheer!). Always look for a Delta IIC rating. It is an expensive test that PROVES how good underlayment is. The cheep dudes will NOT do this test because it proves how BAD their product is. See where I'm going with this? Right. QuietWalk Plus HAS the Delta IIC rating (22 dB). MPGlobal (made by quietwalk....ahem!) does not. For me that's all I need to know...but I also taught myself the insulation/acoustic rating industry. Only took me two years. Yep. 2 YEARS. And I already had a background in human hearing, decibels and neurophysiology of the auditory canal. It was teaching myself the CRAP the industry likes to do to HIDE how bad their products are, that took the longest. But I digress. 1. The QuietWalk Plus has a Delta IIC rating of 22 dB. That's EXTREMELY GOOD. That's BETTER than 6mm cork underlayment with a cork floating floor on top. This is VERY VERY VERY good. Personally I would stop there. 2. QuietWalk Plus is THICKER. Yes. I know. It is ONLY 1mm thicker...but the TOTAL thickness = 3mm. Compare that to the 2mm thickness of the MPglobal. It doesn't SOUND (haha) like a lot but STATISTICALLY it is 30% THICKER. WOW. You have the difference RIGHT THERE. Quiet walk has DELTA IIC ratings that are ranked as very good to exceptional...and it is 30% THICKER. My research is done. I'm still with QuietWalk Plus. I love my cork but it isn't always possible to use it. It cannot be nailed into. Which means my next favourite, QuietWalk Plus is the way to go. Remember: floors are like roofs. It is the ONE surface that takes ALL the abuse. Do not 'save' money on the floor. You'll pull your hair out because you thought a few dollars saved on the flooring would be a great way to save a budget. I'm not saying you are headed in this direction...it's just a statement I always make about floors. I hope this helps....without having to give a two day lecture on the BS of the acoustic/insulation industry. Good luck. QuietWalk Plus is still the best that I've seen. And no, I have no affiliation with them. I'm just impressed with their product.

Ram Board could also play a part. It is the 'tough stuff' they put down during construction to prevent damage to finished wood floors. It's great stuff. Very tough. Just do NOT tape anything to the wood. Tape the seams to each other and then lay the rubber flooring over top. And please be aware that rubber can be tough to work out around. The HIGH END stuff in commercial style gyms has been treated in such a way that it does not off gas too much. The homeowner access stuff can be pretty nasty (low end = $3/sf) with odour and continuous life long off gassing. The high-end stuff ($10/sf or more) is usually too high a price tag for homeowners to buy into. As someone who is allergic to latex and rubber, I can't walk into a tire shop let alone a gym with rubber flooring. The rubber mats are too much for me. I go into anaphylaxes within 10 minutes. Ambulance rides are not the way I like to end my workouts.