You may be able to use the exhaust vent as a chase for pex water supply, but I don't see how you could use it for drain and vent. I think you would almost certainly have to cut into the slab to run the drain and vent lines, at least, so you may as well run the water supply there as well. It's not that big of a deal, since you only have 7-8 feet to go, especially if the flooring is already removed. Cutting a short channel in the slab will generally not affect its structural integrity, but if you have any concerns, a structural engineer is who you want to talk to. Also talk to your local building department (assuming you are remodeling with a permit). $1,500 sounds a little low, but it depends on how easy your plumber can connect into the existing systems. Ask him for an estimate, and get others if it seems out of line.

Chill. I never said you, math, or pictures are lying. :) I am sharing our set up, which is comfortable for us - hate it or love it. We are sharing simply because a user asked, and it works for us. Our facts: I am a mom of two. I live here. I use this countertop every minute. I love it. It is comfortable for me (5’8”). It is comfortable for my husband (6’4”). It is comfortable for my babies (3yo, 1yo). It is comfortable for our guests. I use the drawers everyday - so much accessible storage! We work from home, play games, build legos, feed our babies, make pizza dough, eat, etc. on this counter very comfortably. Our cabin has 18” overhang and we hate it. No one ever sits down, lol. Our home in the city has 18” overhang and we hate it. No one ever sits down and we can’t reach anything inside the deep cabinets even with rolling drawers. I have to get down and crawl to access storage even with pull-out drawers. Super uncomfortable. Our other homes also have 18” overhangs, but we use our 12” overhang the most. IMO, deeper overhang = kids bump their heads more often, more darkness, less accessible storage, takes more valuable real estate, counter is used for eating big meals, do not have a choice to move stools away. IMO, a less deeper overhang = kids crawl under less and do not hit their head, more accessible drawers and storage, makes home brighter, more space for people to walk or kids to run around, host parties where guests can sit if they want or stand if they want, we can move the stools away and place baby high chairs that hang on the overhang, etc. This is comfortable for us and works for our lifestyle.

We added a slightly larger crown molding and molding along the bottom of the cabinets when we refinished and replaced the doors. The pictures below show before and after. We were encouraged by a few kitchens we saw here and on the Finished Kitchen Blog that had added extras to their painted cabinets. I've included a link to one below the pictures. Here is a link that might be useful: Nice painted cabinet re-do

That seems like a good case for rollout shelves to me. I guess it depends on how often you're planing on getting into these cabinets and what you're putting in there, too. I just have shelves in the cabinets under my island overhang but they are very shallow (ranging from 4-8" deep) so it's not at all hard to find things in them. (My cabinet guy does not believe in unused space, apparently.)