Galleys and Ls are my favorite kitchens. I'd take the countertop to counter height. It will give you more workspace, and make the kitchen feel larger.

Is one of the doors opposite the kitchen a coat or linen closet that could be converted to a pantry?

If you have found that you don't use the bar for seating, then your idea to put additional storage there is perfect.

I am just planning to remove the wall in my galley kitchen. You are lucky to have that much already done. In my kitchen the previous owners bumped out a wall to the garage and installed 45" of pantry cabinets (3 15" doors). That could work over where the closet stands now.

If you want to add cabinets on the back side of your current ones, but if you don't want to take up too much room, you could add some that are shallower than the full 24" standard base cabinets.

Taking the cabinets to the ceiling will give you room for seasonal items and bigger items. Ceiling height cabinets also eliminate that space which accumulates dust and grease and encourages you to put stuff there which also accumulates dust and grease. Go to the ceiling; you won't be sorry.