Document level security could be helpful for sure to decrease the amount of manual labor you would have to do probably in a few interesting ways.
Otherwise, your next two best bets would be either a bit of scripting using the API where you can control how you store, load, enable, and activate your rules in any pretty much any way you want to:
You do an export of the rules which would is in ndjson format (http://ndjson.org/), ndjson format is just the rules separated as 1 json message/rule per line and then a single count in JSON format at the bottom of it. You can do a search and replace of your input indexes (or write a script to do it for you) and then you can import that using the UI for each space you want to using the UI.
For imports you can also flip the enable flag for the rules you want to auto enable as well so it's designed to be flexible enough for some of these use cases.
You can also use CURL, POSTMAN, REST based tooling with the imports too, depending on how much manual labor you want to remove vs. manual UI based uploading and verification since imports and exports also have API's: