I'm a very visual person, so thank you to those who are taking the time to post drawings and pictures. The idea of it being "too open" had never really occurred to me in that way. Behind the kitchen is the children's bedroom, and having their door so close could be too noisy. The openness also creates a privacy issue for the guest bath. The angled door off the kitchen is another bedroom which will probably be used as guest space / office. I'm liking the idea Rhome had of using the Twogirlsbigtrouble layout, building a wall to separate all the doors from the kitchen. I also detest corners in kitchens so the idea of having a linen closet (another issue we were having with that guest bath) on the other side is appealing. If we stop at the door in that layout, we eliminate another problem we were having of the kitchen overtaking the living room, but still may have enough countertop and storage. I just feel a need to maximize any available space for countertop. What appealed to me so much about the original design was the designated counter space. Here is a very rough idea we're playing with now. Obviously nothing is to scale and we still need to get the refrigerator in somewhere. The idea is a 4' or maybe even 5' island as long as we can make it without taking over the living room or dining area.

I have a 3.5' by 5' powder room literally tucked under the stairs. The door is only 20" wide. I seriously doubt that it meets code but it was here before we bought the house. The previous owners' son was a plumbing contractor. It does function as what we call the "world's tiniest half bath". We remodeled it a couple of years ago. The hardest part was finding a sink that would work. The best part was choosing tile for the floor. With less than 18 square feet of flooring, even the most expensive tile we liked didn't blow the budget.

30" sink and 24" dw gives you another 18". The sink will be off center although not by enough to look intentional and you aren't going to have much prep space next to sink. You can probably do better.

cut out the size with cardboard or blow up two ballons, I would say 16 since these are minimal. but I can't see your space.