Switch the slider to a door closest to the living room. Extend the kitchen to the door so that the refrigerator is on that wall.

Now you have room for an island that goes the whole length of the kitchen with seating on the side that is now the 'fridge wall.

I think the footprint is ok, but I'd put the dishwasher at the end of the run and extend the sink run so it pushes the peninsula out about 3-4". You'd be able to get a lazy susan base cabinet in the corner to the right of the sink and it would give you more working room. OR put the lazy susan to the left of the sink, but I wouldn't mind two in my U-shaped kitchen (my layout is about the same as yours). OR put a 3-drawer base to the left of the fridge for pots, pans, tupperware, etc. The more drawers you can get in your kitchen, the better.

Do you like having two separate eating spaces (eat-in and dining room) or are you open to combining them to one? If you were open to combining them into one I would up the dining room entrance, extend the kitchen into the breakfast area, knock down the wall between living room and kitchen, and put in an island or peninsula for people to sit around.