Replace Hazy Video Segments

I have a completed 20-minute video (V-1). About eight minutes of it are third-party clips that must stay exactly as they are, but most of the remaining footage suffers from haze and poor contrast. I have... (Budget: $10 - $30 USD, Jobs: After Effects, DaVinci Resolve, Final Cut Pro, Video Conferencing, Video Editing, Video Post-editing, Video Processing, Video Production, Video Services)