According to https://forum.builder.io/t/data-binding-to-content-item-custom-fields/2653/2, there's a way to directly data bind to custom content fields. Would be nice to have a UI for it! Just add fields of the same type to the dropdown menu that pops up when creating a data binding.
Or possibly to allow a flag so that the field propagates or somehow syncs with state, as Tim suggested (although that behavior could be confusing).