If you can't REINDEX a workaround is to use aliases. From the official documentation:
APIs in elasticsearch accept an index name when working against a specific index, and several indices when applicable. The index aliases API allow to alias an index with a name, with all APIs automatically converting the alias name to the actual index name. An alias can also be mapped to more than one index, and when specifying it, the alias will automatically expand to the aliases indices. An alias can also be associated with a filter that will automatically be applied when searching, and routing values. An alias cannot have the same name as an index.
Be aware that this solution does not work if you're using More Like This feature. https://github.com/elastic/elasticsearch/issues/16560