Hmmm, looking a bit deeper it might be possible. See https://developer.wordpress.org/themes/advanced-topics/customizer-api/#custom-setting-types
It appears one can use customize_update_$setting->type and customize_preview_$setting->type actions to build a custom setting object that saves/previews data other than theme_mods and wp_options. I haven’t looked to see if customize.php gives us the post object or if we’d have to build a custom query but it looks promising. I’m very surprised there is little mentioned of this on the webz.