I think you'll find that this will simplify things greatly, and solve your problem. I would suggest using 1" MDF for the shelves (to help eliminate sagging) but otherwise MDF will work fine.
I do commercial cabinetry and have for probably 10 years. We did the Cesar Chavez Elementary school in San Francisco with MDF cabinets sprayed with clear acrylic lacquer. Yes sanding all of our machining and saw marks out of the panels for the cabinets was tedious work, but it can be done without too much trouble. MDF is a great choice for paint grade material, and for paint grade cabinet doors it is far superior to plywood. MDF doesn't warp as easily (provided it is kept in a climate controlled environment) and takes paint much better.
Good luck in your project, feel free to ask questions, and post pictures!
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