Unfortunately, we do not offer a crown molding smaller than the 3 inch tall Shaker or Portland crown listed on the website. 3″ is pretty small IMO.
Technically, you can order the 4 inch crown package from either of the links below and install the crown molding lower on the flat backer. By positioning the molding near the bottom of the backer, you can achieve a visible crown height of approximately 3 inches with no portion of the backer exposed.
This is actually how we commonly installed crown in the early 2000s. The tradeoff is that you lose the flexibility to scribe or adjust the crown to follow the contour of the ceiling. Most ceilings are not perfectly straight and tend to have waves or dips.
If you are installing the cabinets with a small air gap above them and are not trying to tight fit to the ceiling, this approach works perfectly fine.
https://www.barkercabinets.com/product-p/mshakercrown3backer3.htm
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