Is it possible to make delta updates to a single value within a group via the REST API? It appears that I have to include all of the existing data with each item (a custom post type in my case). When testing this any existing values I don't include in the POST get removed from the group.
No, it's not possible. A group saves all subfield values to one row with the serialized array in the database so if you want to update a subfield value you need to have all other subfield values to update along with the group.