Why are you replacing with triple sliding with double (not single)? I am you have thought through this but.... What if you replaced it with standard single door with large glass area (since you have decided to bite the bullet and replace door and spend the money).... I think this will be fine since you have access to the "deck" from the sliding door in the living room. So you still have double access to the deck. Sliding double door versus single door has the exact same access width. The only difference is the amount of light coming in. I think you have enough light that you can do this. I would not do any uppers between the frig and sink to open up the room a little. You could move the frig to that wall, so you have frig, sink, then range on the L going from left to right. This will give you more landing around the stove. I think you will still have enough room for a table in the eating area. Visually, if you are running the cabinets to the ceiling, you need trim that is as wide if not slightly wider than the stiles of the cabinets. Even if the crown is simple in detail, you still need a little more "weight" to balance the cabinets than what is drawn. If you want more modern clean line look (which would not look good with your 6 panel doors), then you can use slab or very plain doors with minimal trim.

We had a similar dilemma when replacing floors in kitchen/family room. Both rooms connect to where we have or will shortly have hardwood floors, so no laminate or vinyl wood-looking tile was even considered. We ended up with Downs luxury vinyl tile (LVT). It is a floating floor that clicks together very, very tightly. You really have to see it in person to appreciate the difference between it and other vinyl---definitely a huge step up from sheet vinyl. It's not tile or slate, but I am happy with the looks and easy maintenance of our floor. If you've had tile before and are happy with that option, that might be your preference. I have had tile floors before and didn't want them again, so the LVT provided the correct option for us.

Styrofoam is a form of polystyrene, a highly flammable compound. I don't believe it is allowed by code in exposed interior locations unless covered by non-flammable materials. In a situation with a house fire, it would melt, emit toxic fumes, and increase the speed of the fire. Here is an illustration of how polystyrene reacts to open flame: Foam board flammability

Sorry I was focusing on the vertical element not the floor, which your question was about. I agree though that you should rip that white tile out. It is terribly dated and will be an eyesore once you have new material for the chimney and the floor around the fireplace. And whatever you put on the floor for a hearth will be yet a third material. Too much going on. So I would just do the wood in the kitchen unless you want tile in the kitchen, in which case you can find a kitchen tile which you can extend to use as a hearth tile too.