Sounds to me like your flooring and trim are close enough to each other, that you are fine with the cabinets being different. I agree that the cabinets can be considered furniture and don't have to match. It sounds like yours will add some contrast to the other woods, which will be nice. I think you are getting good advice from those who say it will look fabulous.

Honestly, I've always perceived of eclectic style as someone who says, "I don't care what you think" and does what they like regardless of convention. Eclectic style is a buzz word in decorating because people get flustered and can't define or label something that isn't easily categorized. In each of your photos above, I can point to what I like and what I don't like--but I bet the homeowners don't care what I can point to. If you consider the philosophical definition of eclectic, it makes more sense: of, denoting, or belonging to a class of ancient philosophers who did not belong to or found any recognized school of thought but selected such doctrines as they wished from various schools.

I can't really tell your furniture arrangement with the pictures provided. Possibly center the rug/rug pad to the tv console and then have at least the front legs of all furniture on it. Then, nothing will slide. Maybe this will help- https://safavieh.com/area-rug-tips

My dad, product of the Depression, always thought you had to have all the furnishings as soon as you moved. So, many of the furniture, paint, window covering decisions my mother made quickly without considering how we would live in the house. My pace of decorating made him crazy (or he thought I was crazy?!). I move, then spend lots of time watching how the sunlight affects each room. Do I need a big sofa or a smaller one with trimmer chairs? Do I need to block the view of the neighbors with blinds or do I want the moonrise to be featured? What color paint is always after I pick fabric because it is easier to match paint to fabric than try to find a drapery that matches already painted surfaces. I shop at antique shops and consignment stores. Decorating my house is not a job that has to be on a time clock. Move in and let the house guide you. Have fun. Let your style evolve. You don’t have to be tied to a style: good design is timeless. Make yourself and your family comfortable and happy.