I am hoping that "modern minimalist" means something different to you than it does to me, because my vision of modern minimalist would require replacing the cabinets (if you are keeping the granite, I assume that you are painting the cabinets rather than replacing them) and the floor, which would require a budget that it sounds like you don't have. You can move the kitchen toward modern and minimal, but you have to work within the constraints of your budget and the things that have to stay. And unfortunately, I don't think that high gloss white cabinets are going to give you the look you aspire to when paired with the floor and counter that you say have to stay. I don't want to rain on your parade, but I don't want you to spend time and money and be disappointed in the result (but maybe your definition of modern minimalist really is different than mine, and I'm concerned for nothing).

I am going to post this and run off to do some visualizations for you to help you see the whole thing together.

I don't know what happened, but there was a response from the OP that disappeared along with a draft of a response from me.

The OP said they were getting new cabinets and the contractor thought that he could salvage and reuse the granite, so that's good.

I did some not very professional-looking mock-ups, one with a greige back-painted glass backsplash that works with the counter but not the floor, and another with a bright white back-painted glass backsplash.

Do not do a high gloss backsplash (in any color). You already have shiny floors, counters, and soon to be glossy cabinets. Do something matte or textured for the backsplash. Also be careful to select a white for cabinets that works with counters and floor.