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.

Demo. I'm never had bamboo flooring but, besides the concerns about making a moisture sandwich to rot and mold, I would be concerned about the expansion & contraction of the bamboo underneath the rigid overlay. What I understand about bamboo is that it is more wiggly than wood. Since you have engineered bamboo, probably doesn't move as much as a solid product would. There are other reasons to remove it--like avoiding having to undercut door casings and shorten up doors. Removing baseboard or compromise by having it buried behind flooring. Probably other reasons that I'm not thinking of, too. I would pry, scrape, whatever it takes to get it up & haul it to the firepit to get rid of it. There are going to be about a hundred responses telling you not to burn it. Fortunately, none of 'em know where I live. :-)

HI everyone, thank you all so much for your thoughtful input! The overall theme I'm seeing is to not refinish the hardwood just for the sake of doing it - and definitely not for the sake of matching the LVP. For some reason, I didn't realize this was an option (lol) - I have been getting so bogged down in needing to take action (a la my husband with the kitchen floor), that I didn't even think to take a breather and let it be for a while so we can re-gather our thoughts :) And since the hardwood will be getting done in the next year or two anyway, it feels almost like a weight is lifted off my shoulders with not having to add one more thing to our current To Do list! @kempek01 your suggestion is spot on and made me laugh out loud! Truthfully, the mismatch didn't bother me as much until I thought of what my in-laws would say at our housewarming - and really, all of them are homeowners, so I'm sure they understand the concept of a work in progress ... AND if anyone does comment, I will say "Thanks for noticing" and chug my wine (while mentally throwing it on them)! @Patricia Colwell I like your idea of having the same wood species laid down in the kitchen and all of it matching! Or the idea of vinyl tile ... honestly, I was thinking of anything besides the LVP my hubs came home with! Lol! but having the same species of wood all the way through the house would be a very charming look! @dan1888 thank you for your words of wisdom! you're right, no need to sacrifice the rest of the house's hardwood to coordinate with a not-thought-out temporary fix :) @SJ McCarthy you make so many good points ... we're also in the middle of a total bathroom renovation and a light second floor renovation (which will then be further renovated down the line anyway), so the last thing we need to be thinking about now is moving our furniture from room to room, or to a storage pod, so the floors can be refinished. And, while we know we want to refinish them, we haven't nailed down a specific stain yet, so it would be more rushing, potentially leading to more regret! Your suggestion of sitting down and storyboarding each room is soooo incredibly wise ... we will definitely be doing that, starting over dinner tonight! @Fori thank you so much :) we think it's super cute too! It really is charming, and in keeping with the style of our house. It's so funny you say that, because my husband (he is a darling) EVENTUALLY wants to gut the whole kitchen, knock out the back wall, and expand the whole kitchen/dining room area!!! However, that's a big expense and still quite a few years down the road - plus, I think the house is kinda sweet the way it is - but the lack of dishwasher does plague us when we have guests for dinner! Ha! Anyway, I guess there's no point in paying twice for a temporary kitchen floor (and staining the rest of the house to match ...). Phew! I feel like I've been talked off several ledges today!!!

Traditionally (ie. by a pro who is paid to do things well/properly) the damaged substrate is removed and replaced. Patching is possible if there are minor spots that just need 1-3mm of fill. If the whole thing has a shredded surface then it is probably easier/faster to remove and replace with the same thickness. As G&S suggests: photos please.