I had the same problem. Had old strip flooring that was over 100 yrs old. At one point someone replaced a section with 3/4 thick wood floor but you wouldnt know until it was tore up. When I laid all the flooring an got to the the hallway I was up about 1/2 in. I shimmed up an 1/8 in then stripped a blank of the new floor on the table saw to build a thin transition piece. There is a slight raise but everything is the same level and looks nice. So in short just use a reducer.

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.

Yes, it's one of those single floor constructions...3/4" T&G fastened directly to the joists. Since the house is balloon frame construction, you might be safe just removing the existing T&G and installing new in place of it. That is what I would do, if it was my house. That way you change no finished height, the stair cadence is not affected and you can add sound deadening unfaced insulation in the cavity below. Any sound attenuation efforts are going to have minimal results whatever you decide to do. If you decide to replace the single floor construction, make sure the strip flooring you purchase for the project is the longest lengths you can get and are milled for a good fit (you want as little 'play' in the T&G as you can get). Also, you may have to add some additional blocking here and there, especially adjacent to an exterior wall edge where there may not be sufficient support.

It's splintering and cracking because it's maple - hard, durable and brittle. And prying boards up is guaranteed to destroy them. You have to remove them by reversing the motion it took to install them. The screws look like the easy way out, and the least expensive, if you haven't reached the point of no return on the removal. If you want to salvage the wood - and it's selling for $5+ per square foot as salvage - buy an oscillating multi-tool and several metal-cutting blades. Slice through the nails under the boards and coax the board loose. If you can work from the side with the tongues, the nails are accessible and the boards easiest to remove. It's faster, and easier and saves more boards. Remove the molding and use a wood-cutting blade on the multi-tool to slice out around the cabinets, but accept that it's going to be difficult to impossible to do a clean job, and the new floor will abruptly end at the cabinets. If appearance matters a lot, remove the cabinets, take up all the floor, put down the new floor and re-install the cabinets.