The problem is that KCC relies on KindleGen for conversion, which creates dual-MOBI files
dual-MOBI contains both legacy MOBI and the newer AZW3 (otherwise known as KF8).
calibre only knows how to modify the exth fields for the MOBI component, but your Kindle is reading the AZW3 component.
You can use
KindleUnpack to split out the AZW3 -- I think there is a FAQ entry about that somewhere in KCC's instructions.