If you are skilled with a grinder, you can cut the tile and carefully break out the material you don't want; the difficulty will be that you can't take the cut all the way to the back wall because of the shape of the grinding disk...unless you cut into the wall a bit. Alternatively, you could have the bottom edge of the additional cabinet trimmed the thickness of the tile installation and have it sit on top of the tile and be the same height as the other cabinets. This would possibly be easier for an installer to do than cut the tile.

I hope you painted them! Everyone is suggesting a pro, at the low, low price of $7k. And if I hired a pro interior designer, I'd expect them to suggest a pro - which I'm sure would do a great job. But, if you want your cabinets white, paint them! If you're anything like me, you'll never be satisfied until they're white :) I've painted our kitchen cabinets at both our houses and they turned out great. If you sand, do the prep work, and buy quality paint they will be fine. We just redid our kitchen and the brand new cabinets looked blue instead of charcoal, so I tried to get used to them for a year and hated them everyday, until I repainted them black. Never regretted it once. That's the best part of owning your house, you can make it however you want it with the budget you're working with.

I see them painted on site on the HGTV shows. HGTV is entertainment, not a place to find the proper way to do home improvement. They only care about making things look good for a final reveal, not doing things correctly, or making things last. Maybe you could ask your friend about finishes he would recommend? People, I believe, often use "paint" to mean a pigmented or colored finish, and "lacquer" to mean a clear finish. Actual paint and lacquer are at the bottom of any list of products to use on cabinets. The only benefit to them is ease of touchup. You can still have a decent finish applied to installed cabinets, but you will need to ask for it, and probably pay more for it.

@ Ricky Aime - I strongly suspect that you are out of your depth here and need to slow down a bit. Take some pictures on your phone and post them here and describe the problem rather than the conclusion, because nothing you are saying makes a lot of sense. The stove is not standing evenly on the floor. You can literally see floor is not even. Ranges typically have leveling feet that can be adjusted independently. You can adjust the feet so that the range is level and doesn't rock. There is no need to reinstall your floor to fix that problem. I need to plug any holes behind the counter and the dishwasher. If you are concerned about pests than plugging the holes will be about as effective as putting up a "DO NOT ENTER" sign. The most effective way to control pests is to control the reason that they are coming into your house. Mice are pretty effective at getting into your house and covering a few holes that they are currently entering is not even going to slow them down. In fact, you will likely spend more time covering the holes than they will getting around your detour. I have ceramic tiles on the floor that cracking and need to install hardwood floor instead. If you have cracking tiles you likely have a problem with deflection (your floor is not stiff enough). Combined with wavy floors (which is what I assume you mean by "you can literally see floor is not even," we can guess that you probably need a better subfloor. True hardwood floors can typically handle a bit more deflection when installed across the joists, but you may not need to remove your cabinets at all to install hardwood. It really depends on the toe kick of the cabinets and the particular details you are dealing with.