Getting on a ladder to clean, sand, prime, and paint that crown is a massive undertaking. Or pretty darn expensive to have done correctly. Sure, you can hire the "$100 a room" guy to ruin that, but that will come back to haunt you. I would leave it be until you plan more changes for the whole space. Just painting the cabinets that I see would be a 15K-18K job from a pro cabinet finisher.

You can definitely split the crown color. Paint it the same white trim color around the room and leave the sections connected to the cabinets in the brown stain color. You see this in many kitchens, so not unusual at all.

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I would absolutely paint the crown on the walls your white trim color and leave it wood on the cabinets.

Compared to proper prep and paint, it's less expensive to rip and replace.

Rip it out, replace it with the profile and color you want.