I think I have managed to solve my own issue.
Before, when I had added the new layer and the new distro and machine configs, I had just 'hacked' / modified the bblayers.conf and local.conf files in my build/conf folder. I manually added the meta layer to the BBLAYER variable, and manually modified the MACHINE and DISTRO default values in the local.conf.
This apparently is a bad idea; even though it is sort of what the NXP / Freescale Yocto Project User's Guide suggests.
What I have now done is the following:
1. deleted all files in my build/conf folder
2. manually added my Meta layer to the place where it generates the BBLAYERS variable in fsl-setup-release.sh
3. re-ran source fsl-setup-release.sh:
DISTRO=fsl-imx-customdistro MACHINE=imx6sxcustommachine source fsl-setup-release.sh -b mybuild
4. run bitbake -c cleansstate core-image-minimal
5. run bitbake core-image-minimal
This seems to sort out the mess. Clearly it is just a scripting tangle issue that is going on.