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.

IMHO that's a good way to be told "Only install at exactly this temperature and within 2% of this humidity and on a floor that is level to 0.0001" and leave a 1" gap or we will void your warranty."

So what are you having as the FINAL floor? It sounds like you are installing 1/2" cork FLOORING TILES....but then a little further on you are talking about wood over cork. This tells me you are talking about cork UNDERLAYMENT underneath hardwood. OK. Now we are on to something. A vapour barrier is required if you are AT GROUND LEVEL or BELOW. Your installer can glue down the cork to the SUSPENDED SLAB (aka....10th floor concrete slab) without worrying about a vapour barrier. A sheet vapour barrier is NEVER USED with glue down anything. The glue must act as the vapour barrier. Glue down hardwood over glue down cork underlayment is a MAGNIFICENT floor. And it is one of the MOST EXPENSIVE installation formats for hardwood that we have (yep....it is more expensive than you can imagine). If your engineered wood can be FLOATED then you will save HUGE amounts of money (could be as much as $7 - $10/sf worth of savings). The cork can be floated (it just sits there....no glue) and then the wood is floated over that (glued at the edges and tapped together). It is a MUCH faster installation (can be 2 days faster). But first: what floor do you live on?

G & S beat me to it. The TOTAL cost = $2200. That includes materials, labour for removal of the old, labour for the primer, labour for the application of the leveler. I've often suggested that subfloor prep be seen as a range from $2 - $5/sf. Condo's with nasty/cheap gypcrete floors = higher range. High-end leveled concrete slab in a multi-mill home = lower price. The easiest way to 'swallow' this is to divid 2200 by the total square footage. If it fits inside the $2-$4/sf range, then you are in good shape. And to be clear, this type of leveling is required for EVERY rigid surface floor (wood, laminate, cork, vinyl, tile, stone, etc). The only surface that gets away with a wonky subfloor = carpet. I'm sorry you have been shocked by this, but you have REAL PROFESSIONALS! I'm not kidding. There is no 'tongue in cheek'. I mean it. The IDIOTS who want to rip you off, would have swept the floor and laid your wood. They would have run away with all your money and then changed their phone numbers when you tried to complain about how horrible your floor feels. Please take a breath. I know this hurts. It is SUPER important for this work to be done. There is no way around it (unless you stop and put in carpet). Thank your pros for telling you about the work needed and make sure they have some treats for those days they are working on the subfloor. Subfloor work is a PITA! And NO ONE likes to do it (that's why most 'dudes' simply take your money and install what is on hand). It would be nice if you chipped in a treat to show you appreciate their honesty and their effort. You have found ONE out of 30 'pros' who would tell you about this. The other 29 would take your money and never look back.