I have removed pieces like this with a sawzall. Remove all the screws you can and make 1 or 2 cuts down through the center It should give you enough room to pry the piece out without touching the cabinet. Divide and conquer.
A forum community dedicated to Do it yourself-ers and home improvement enthusiasts. Come join the discussion about tools, projects, builds, styles, scales, reviews, accessories, classifieds, and more! Helping You to Do It Yourself!