Ahem. I believe flex aluminum ducting, as the above image appears to show, is prohibited for grease contaminated ducts. They have to be steel to resist fire penetration. Even if one chooses to ignore code, for safety's sake please routinely inspect and replace if build-up is detected. Alternatively, if the ducting were surrounded by steel in both cavities -- such as metal on all the cabinet surfaces -- it might be passible.

I have a slideout vent hood now. It doesn't have the cabinetry trim, though. It has about 1.25" of black showing when the hood is tucked in. I really like the thing. It has good capture, it doesn't have a presence in my small kitchen, it bounces back when the tall spouse bumps it (less cussing!), and it's easy to use. So don't worry about the slideout being a hassle. It's not! In fact, we'll be replacing it with another one (probably the GE Monogram). I really like the thing. And now I'm going to be taking a second look at the Imperial ones. I don't see why you couldn't use a trim piece with more shape to it.

Most slide in ranges come with a stainless filler piece for the space between the range and the wall so you wouldn't need to purchase a piece of counter for that area.

The Minimizing Range Hood article repeats an error I have been preaching against for years here because it leads to misunderstanding of hood requirements. The article states, in part, in the portion titled In the ceiling. "Another option for above an island is to select a range hood or exhaust system that can be built in flush with the ceiling. These hoods are generally more expensive, as they need to be extremely powerful to suck up greasy air and odors from such a distance." Hoods that anyone could stand in a kitchen environment do not suck up the cooking plumes beyond a fraction of the hood's shortest base dimension. They utilize the cooking plume's upward velocity to get the effluent to them where they can collect it. Then they use their blower strength to get the effluent past the filter and expel it from the house. Otherwise the plume would mostly reflect off of the filter and flow back into the kitchen. This is why the size of the hood entry aperture is important. In a ceiling application, "extremely powerful" is still correct, but it is due to the large area where the air velocity has to be high enough to get the effluent past the filter area. The large area results from the expansion of the cooking plumes as they rise. What the ceiling application touts do not make note of is the effectiveness in the presence of inevitable cross drafts, and inconvenience of filter cleaning, particularly when the cooktop is Ceran, and the counters are stone, and concentrations of human weight put them at risk.