If "ranch trim" is really short with just a radius edge, then it's what we have in our living room, hallway, and a couple bedrooms. It's maybe 2" tall. It looks much better to paint that trim the wall color, which then means paint anything on the wall the wall color. Also, I wouldn't worry about trying to keep them consistent from room to room. The goal would be to paint them -- in each room -- in whatever way would help to camouflage them best.

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Your inspiration photo is handsome...but it has a much lighter floor and much lighter walls. And the light filled VAULT that highlights the wood is something you are missing. If you attempt a match like your the inspiration you are going to create a very dark looking space. The oak is very 'heavy'. That's a lot of trim that will be stained. And to get it to look good, you will have to go dark. Not medium....dark. Your floors are quite dark (we rank them as 'dark') which means your tone on tone match is going to be dark. Are you leaving the houses trim WHITE? I would keep the trim and the stringers white. I like the idea of the hand rail matching or being DARKER than the flooring. Your newel posts could be white - same as the trim. Or BLACK. Just be aware you have Red Oak. The red is going to be tough to get away from. You can use Jacobean to get rid of the red AND to darken the stain. But be careful with all the heavy trim work on the stairs. They are going to be powerful if you go dark. It will look very, very heavy.

Since you have experience painting over the floor tile, why don't you paint over the countertop, too. There are products made specifically for that specific purpose. If you want to keep the peach, I'd paint the entire room a color of white that works with the trim/cabinet/floors, and accent with navy blue rugs and towels.