It sounds like you have several issues: A) Squeeks B) Cold Floors C) Concern about floor level differences Regarding A, the builder is basically correct - 3/4 OSB is a building standard now. It is tongue and groove and glued down and together. Over time is will begin to squeek. You know where the squeeks are and when removing existing flooring, nail the subfloor tight again. Should eliminate, or at least reduce the squeek. Regarding B, See if you can have foam insulation injected into the cantilevered space. As to heating, it still may be necessary but why not minimize its burden by controlling the root cause. Regarding C, Several things here. Your current vinyl should be installed on a thin underlayment. Combined they are about 1/4" thick. It will be necessary to remove these. (This will be the time to inject foam insulation) A tile floor needs 1.25" minimum structural support which means a 1/2" thickness of concrete board will be cemented and screwed atop the existing subfloor. Then your heating mat followed by tile. So, you'll be gaining about 3/4" above the current level. Your tile shop will have a marble threshold with a beveled edge to minimize this effect. We have this same situation is our home and it is negligable. You may or may not have to trim the door. Base trim would be removed in the bath to do this work. It can then be reinstalled, replaced or have the tile setter install tile as base trim - that's what we did. Here is a link to an updated bath we did and amongst the photos you can see the threshold and tile base trim. Hope this helps. Good luck. Here is a link that might be useful: Bathroom

My guess is the odor is coming from the walls. As worthy mentioned, I'd think the epoxy flooring is non-porous. For cleaning, use only products made for kennels and specifically for cat urine. You can try cleaning the floors and wall with the enzyme, let it dry thoroughly, then seal with shellac. Before spending money on replacing the floor, I'd try to determine if the walls are the problem. You should buy a black light first, since it will show you the areas that are soiled. Remember that when using the enzyme, you need to let it soak for hours for it to work well. In addition, don't use other non-enzyme products on the odor since it prevents the enzyme products from working efficiently.

@S Rodriguez - Good point. Will have to check. @Jmc101 - Responses below: No refrigerator. While it is not depicted, I intend to have a small refrigerator either in the cabinetry under the stove or as a stand alone. is "Storage" intended to be the ONLY storage for clothes and linen/towels? What about a dresser? Mmm...yes. I had not thought of a dresser. There is room to expand the right wall, behind the area marked "storage", further into the basement. However, due to the vents behind the wall the ceiling height would be lower than the rest of the room. is there additional storage outside of this room? The rest of the basement has a lot of empty room but I wasn't planning on giving any additional storage to the occupant. There is no room to move between the counter and sink in sketch 2. The sketch is not drawn to scale but that is a valid point. Need to double check. is the only access through the sliding door? There is a door (first pic above) which leads to the basement and the laundry room. However, the sliding door (which will be replaced by an entry door) is the primary access.

I completed a similar kitchen remodel last year. I did use a counter depth frig. It ALL totalled just under $10k. DIY. Ruvati sink, Kohler Worth faucet. Dal porcelain floor tile & backsplash. Liberty Bundled Reed handles. Kraftmaid rope crown moulding. You could use different granite or color combos. They had tons of Class 1 granites to choose from. The floor is porcelain tile in a patio design. The cabinets are RTA. Just to throw some ideas out there for you. --------------------------------------------------------------------------------------------------------------- Here's one we did the year before, it was also under $10k: It has a butlers pantry back in the corner. I saved money on the frig. by going w/ a standard depth.