John, I tried your boiling water trick and it worked! (As a bonus, all the water should help prevent asbestos fibers from flying around.) @ci-lantro, I may try your trick too to see if it pulls the tile up all in one piece. So far I'm still pouring the boiling water on the stuck-on backing that won't come off the hardwood. So John, what did you do once you pulled up all your tile? Did you feel okay about sanding your floors? We'll definitely need to sand and that's the only part of this process that worries me health-wise.

The most recent photos....the TOP pic shows a VERY DARK slate looking product at the TOP of the picture (nowhere near the wood sample). That's the type of product I'm talking about. It looks like you are still pulling HEAVILY towards the white-with-gray-veining products which do NOT like to work well with Brazilian Cherry. Your "want" for gray is making the decisions very very difficult. The sales people in the shops will "sell" the most popular products. And right now those are gray/white products. That's why you are having a more difficult time. You want gray. The SALES people want to SELL YOU gray....which means you are pulling a WHOLE BUNCH of gray products that aren't working. Your floor is BUSY...because that's the stunning part of Brazilian Cherry. It is stunning. It is fantastic. It is brilliant. It is BUSY. It is a DIVA! (gotta love them for it!). And only ONE DIVA is allowed on stage. So....your floor tile choice will be a SUPPORTING ROLE. Something calm and reserved. Try to stay away from tile that has a lot of movement or VEINING....it will compete with your Diva and the two will get very upset with each other. suzyq53 has an excellent suggestion: limestone-look porcelain tile. You do not have to have STONE to have the LOOK of limestone. You can have porcelain tile limestone looking product. Limestone is a pale cream/yellow/beige colour palette that works very nicely with wood. It will keep the tile area LIGHT (which seems to be part of your drive...even though a dark slate-look would do very well with the stairs/banister). Go ahead and google some of these products, down load some photos onto your phone and then take THEM shopping. That will trim down the "sales pitch" from the sales people. Do you have a designer you can work with? They will help speed up the process by a few weeks.

If you're hesitant to do wood due to durability, or attempting to match the rest of the house won't leave you a seemless transition, you could use a light natural Stone to maintain brightness and still add some warmth to the space

The "oil finishes" are hardwax oil products that are applied as a single coat. They are traditionally a matte finish and they require maintenance by the homeowner. You must be prepared for the maintenance. Many of the factory finished engineered floors with oil finishes can require (or would benefit from) an application of maintenance oil applied as soon as they are installed. This isn't a huge issue (because it is relatively easy) but it is something that most people do not know and therefore "miss" the opportunity to add this little bit of extra love at the beginning. Once installed, the oil floors are beautiful, raw-looking wood finish. They are low gloss. If you are someone who likes the look of a "clean shiny floor" then you will be horribly disappointed by the floors and will spend days and days trying to "clean" the floors to a "shine" - without any success. Tears are soon to follow. As for "UV oil finish" this is just a fun way of saying the factory used UV lights to speed up the curing of the finish. Instead of 2-3 days, the cure can be reduced to a few minutes under UV lighting. That's it. That's the whole difference. Other than that, UV cured vs. natural cured hardwax "oil" finishes are the same beast. If you love the look of oil finished flooring, then go for it. But PLEASE FIND OUT the maintenance requirements and purchase ALL of the maintenance products at the same time that you purchase the floor. That includes any "colour oil" products used to create the colour at the factory. Once the floor has been delivered, I would find a "culled" or warped plank (an imperfect plank that will not be installed) and start playing with your maintenance products on the board (or boards) so that you are well schooled BEFORE a little "oopsa" occurs. It will make your life MUCH easier.