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.

Di you check with the manufacturer? The manufacturer of my flooring had specs and recommendations for glues. My installer said that all installers have their preferred products, so I used something that the manufacturer recommended and that he was also familiar with and comfortable using.

The reviews you're probably looking at are the low priced levels when 'locking correctly' is mentioned. If you offer a budget level you'll get far more opinions. Otherwise it's a wild card game.

We are planning to replace flooring throughout our house as well, 2900 sq ft. We currently have 20yo tile and carpet that our new dog has had accidents on. We are trying to budget and also debating btwn hardwood, porcelain wood look plank tiles , or engineered vinyl luxury plank. Any thoughts on Engineered vinyl. I’ve read feels/looks most like wood, is waterproof (rather than water resistant) , doesn’t dent from weight of furniture is pet friendly, and cost less than real wood and tile. My preference is tile due to pets and water , but most likely cost prohibitive due to labor intensive/cost. Hardwood not pet friendly or moisture friendly in kitchen , guest bath. We have a very open floorplan where we cannot separate flooring from kitchen and bath. BUT i’ve also read that you do not get ROI on vinyl flooring, even though a designer told me she is installing Luxury vinyl in multi-million $ homes these days (I am in S. California) Any advice appreciated