Removal and re-installation of windows is not all that difficult just need to take your time with some good pry tools. If the louvers need replacement you need to partially remove the windows anyway. It allows you to clean up the window openings and get rid of all the accumulated dirt and debris.
Leaking Vent Louvers is not a common problem but the molding trim pieces have seals around the clips that fail which is most likely your issue. As they age they harden and deteriorate allowing the water to ingress. I would remove both rear sliding windows and check for rust issues.