We currently take an "incomplete" backup that doesn't include indexes, which means that we need to recreate the indexes before loading the backups. If we took a "complete" backup that included the indexes, then we would just need to trigger the reindex and we would have a fully working Solr instance to work with.
(There may be some downsides to this approach, such as being able to reconfigure the index after the backup is built, but I think the benefits would outweigh the costs.)