Not sure what your budget is, but one option is to rebuild the front covered entry and have it span the entire width of the house, and consider repeating this basic form in future additions such as a garage if there isn't one already.

Excuse my duh-ness but i'm having difficulty trying to follow whats going on here. Are these two photos an exact replica of your house and pool ? If not a hasty sketch with dimensions could help a lot. By kitchen wall do you mean the wall behind the bar ? And where is the pool wall ? Are you considering the covered area as being "inside" ? Sorry for all those questions lol Sometimes when you have a design problem you need to turn it inside out or on it's head. If you can't beat it maybe embrace it by making a feature of it : i.e. contrast by having the lightest colored pool surround and a great blue or tile inside and under the overhang, something that will echo the water color ? If you have a great covered area as in photo you'll most likely be spending a lot of time there and it could be soothing to be able to sometimes retire into a darker inside. In my book, 10M isn't small and also contrasting two floor colors doesn't necessarily make a space seem smaller and confined and may in fact even open it up. Could it be that you've thought yourself into a box here ? Sometimes one needs to give it all a good shake up and see how it resettles.

Lighting - pendants over the servery bench should be another feature that complements your chosen kitchen surfaces. So whilst I love the copper pendants in picture 1.. They could work depending on the rest of your decor and would be a highlight in a neutral white/timber kitchen = Good! If you choose copper you would complement it with a couple of copper bench top items. These are beautiful! (I collect copper because I love it, my kitchen pendants are silver, I renovated to sell in the next 3-5 years) You will see a picture starting to form in your mind and there is nothing wrong with making a statement with your lighting. I found that when I wasn't sure I would get a very strong sense of what was right and what was wrong for a space, then common sense or passion would determine the outcome! Here are another couple that might work, look her on Houzz under lighting, search pendants, then have fun looking!Timber tones with black or white to complement your cabinets... or Statement white pendants for a bit of quirky fun! Your personality can be reflected in your lighting and accessories creating that point of difference from the predictable white on timber look. Plus don't forget the power of greenery to punctuate the theme!

Do you have a photo of the front of your home? That usually helps when it comes to colour scheme questions.