I understand the struggle. What your doing to customize the Base Layer Picker sounds like it should still work. The only modification you will need to do is update the thumbnails. Since we got rid of STK World Terrain from the Base Layer Picker, we also got rid of STK.png since we didn’t need to show it as an option anymore. Now there’s CesiumWorldTerrain.png for the new Cesium World Terrain. You could use that instead, or get a copy of STK.png from one of our old releases and host it on your site if you still want to use the STK Wolrd Terrain until September 1st.
Thanks,
Gabby