Do you want the whole scheme to be perfect? There's no right answer, it's personal preference.

It would be helpful to know where you want to add blues since you don't plan on changing the interior wall color, and which rooms have a beach view. I think the colors outside have an effect on those inside.

Your house looks beautiful so far. I think you're trying to approach this too cerebrally. Unless you're Lori Sawaya, the color guru, you just have to look at the colors next to each other and see if they coordinate or not.

If you're lucky, Lori will see this dilemma and weigh in. Otherwise, you can go to her website and engage her services: https://thelandofcolor.com/get-color-help/

Which room is SW atmospheric?

I like the walls. I don't see the need to reprint, unless you really hate the neutral. I like the furniture.. Are you keeping the rugs? You need coordinating pillows , not just solids. Find a pillow or two with blue and red that will marry the seating with the red patterned rug.

examples:

https://www.potterybarn.com/products/navin-print-lumbar-pillow-cover/?cm_src=rel

https://www.potterybarn.com/products/dara-print-pillow-cover/?cm_src=rel

https://www.buyfabrics.com/p62675_daloni-autumn-ikat-upholstery-fabric-by-swavelle-millcreek

Mix the scale of pillows, large, medium, small or solid.

OR.... Find wall art in your colors, and solid pillows will marry the two areas (wall art & rug)

If you desire a cohesive color scheme, you must be disciplined when shopping. If ithe item is not in your palette (red-light blue-white), you must put it back.

If keeping the red rug with blue accents, then mix the throw pillows to those with different patterns