The problem with deleting the __Current__ folder is that if you're in the middle of a Dungeon in SP, save, quit the game, delete __Current__ (so that MP will work), then go back to your SP save sometime later, enemies and items that were killed or taken will reset to the scene defaults.
It's a pain in the ass and affects my system regardless of Indexing Service running or not -- I'm still looking into workarounds that don't involve deleting __Current__ but haven't found any yet..
Edit:
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Oh wait, I found the solution.

Enabling the Indexing Service never fixed it for me, but apparently, just enabling and starting the indexing service isn't enough..
I enabled & started the service, then set the "Allow Indexing service to index..etc" property on my Drive E: (where Redemption is installed) (only for drive E:, not recursively) and the Redemption root directory (recursively).
After that, Redemption worked fine.

The indexing service can be a resource hog, so I'd recommend to only allow it to index the Redemption directory (recursively) and disable it for all other drives and their subdirectories.