I agree with you the pillars are unfortunate. The replacement tiles will stand out no matter how close they come to matching so you're better off making sure they are clearly different so the gray one is better. Putting busy mosaic tiles could look nice but will interrupt the flow between rooms which I'm guessing is your problem with the columns in the first place. You will need to create a dextrous solution to tying into the 2x4 wall on the left side but I think it can be done tastefully- maybe beveling it back once you get past he end of that wall.

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.

after watching my daughter and her husband agonize over the way their expensive timber floor has not held up well after 3 years, I would recommend tiles/wood look tiles with under heating. Their beautiful warm expensive floor looks like it always needs a clean and polish, not from neglect, they have cared for it well. One of the boards now has a slight and painful moan when it's stepped on :-( I grew up in a completely wood floor home and although it looked wonderful, my Mother hated it. ....and the mats ! Wood is a lot harder to maintain than tiles ,(no matter what the die hards say) the modern wood finishes are much better than they used to be.... But a piece of wood is rather arty no matter what it's used for and it does demand to be loved and cared for.....and if something goes wrong it's a lot more expensive to fix than sand and cement. Ultimately you have to be happy. BTW underheating tiles is warmer than timber :-)

I do not have any tiles in my current house but if you think about grout discolouring and looking bad.... then I think that might answer your question. My thought - the less grout the better.