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.

Sheet vinyl....it is the only thing that will prevent cat urine from getting between the planks. Sigh. I know that isn't what you were hoping for, but it is the solution that works for leaky pets/humans. Anything that comes in a "plank" runs the risk of urine seeping between two planks and staining the SIDES of the planks. Sides of planks are things that cannot be 'cleaned'. Thereby allowing the urine - and the odour - to remain for the life of the floor. If there is a particular PLACE where the cat(s) will have a litter box (which is where they 'miss') then I would ensure a continuous surface product would be used in that space (sheet vinyl; epoxy that runs up the wall to create a continuous surface up the wall by a few inches). If you mean the cats urinate in random places throughout the home, you are going to be in a bit of a pickle. Pretty much any place you lay 'planked' floors will run the risk of a permanent stain/odour that originates from between the planks.

Kim,,,it's very solid. just make sure the glue is spread to completely cover the plank. I have a few spots (like under the kitchen sink) where they missed the corner and it squeaks. They've held up great. I don't have dogs, but I have cats and have heard their nails burning rubber across the floor they go off on their tangents. I've spilled water, cleaned up their barf, spilled food, whatever, it all cleans up very well. as for dents, only if you drop something very heavy. but any wood floor will dent. I vacuum w/a Dyson, and then I use Bona wood floor cleaner on a mop. in the kitchen, i'll often take the scrubby brush and watered down Dawn to clean up spills or oil stains. no problem. no, I don't baby them. I don't wear shoes in my house though. I love my floors. just make sure on install they clean up all the glue residue. my guys were messy and lazy. had to call them back w/special glue remover and rag and go over the entire floor.

I was in a similar situation and was rethinking my initial choice of LVP, wondering if instead I should get engineered wood. I did lots of research on the pluses and minuses of both AND then I visited the floor store to take an actual look at what I would be getting. By the way, I only visited real floor stores, not big box stores. The decent quality engineered wood (the only kind I would even consider installing) was a lot more expensive that the top-of-the-line LVP I was considering. The saleswoman told me how much extra getting good quality engineered would cost me (lots!). I stuck with the LVP and am happy with the decision.