Love your inspiration photos and the gorgeous saltillo kitchens here! I have a saltillo-lookalike porcelain tile floor. (My floor is probably on the red side with less of the orange/peach tones). I think a creamy white cab color would look gorgeous with the tile. That was something I'd planned to do if I'd stayed in my house. My paint color is Valspar (Lowe's) Epic which reads khaki or earthy green or taupe depending on the light. It's a great warm, interesting neutral. A couple of photos (sorry for the poor quality...they're from the phone). It's an overcast day so little natural light. First shows wall color with floor. Second photo shows wall color with white.

Boone, a stone that picked up the warm tones of the earthy surfaces in a soft way looks very nice in that picture. I'd like to suggest counters the same color as the lower cabinets, in your case a white, with little or no patterning. The simplicity that allows lines to flow and focus to fall on other features has always been very pleasing to me. Downplaying the counter's one of those things that's never specifically in style (especially in these break-the-bank-on-the-counters days), but it's never out of style either. Professional decorators have always done it, and you often see it in expensive magazines. Then maybe echo the Saltillo/brick color in a backsplash tile to tie in with it and the stove area. A lighter version of the same color, perhaps, rather than just accents? In any case, the simplicity of the counters would allow more latitude for the backsplash. Note the way on this first photo that two feature materials, brick and wood, are played off against the white, and how both are carried through the kitchen. [Traditional Kitchen[(https://www.houzz.com/photos/traditional-kitchen-ideas-phbr1-bp~t_709~s_2107) by Mount Pleasant General Contractors Phillip W Smith General Contractor, Inc. [Contemporary Kitchen[(https://www.houzz.com/photos/contemporary-kitchen-ideas-phbr1-bp~t_709~s_2103)

Here is a link. It's for a specific company but should give you some guidelines on care and maintenance of your tile. https://glaze-n-seal.com/seal-maintain-saltillo-mexican-tile/

Geoff, all white would look terrible. I'm not a fan of saltillo tile in general, but yours compliments the ceiling and gives a nice contrast to everything else. I suggest keeping the flooring as is until you're ready to replace.