I went back and looked at your pictures. Couple thoughts -
Push the whole part adjacent to the living room(?) out. Maybe make the dining room side your breakfast bar.
Is your stove gas or electric? If possible, either move the existing stove up against a taller wall to cover the back, or if you can swing it, look at some of the newer designs that have controls in the front, and don't have the tall control board in the back. Many of those also have convection ovens, which are very nice.
Leave the Breakfast Bar at countertop height, like I think Slimshadie said. That way, the whole surface is one height and can be wider if you want, because you need to have an overhang on the seating side (ours is 12"). Makes for more efficient use of the countertop. They do have shallow cabinets for that purpose, which would leave the width consistent with the other counters. Ours is that way, with the backs of the cabinets finished.
Always remember the position of the refrigerator, stove, and sink to each other. They say a triangle pattern is handy. Don't know if that's really the case in a small kitchen like mine, or yours.
Good luck, my friend!!