Good morning! I've been having that same struggle for at least the last year with Camtasia and had finally given up hope. UNTIL I found this post a few days ago hoping to solve a different issue. I made the switch on my display color from Color LCD to sRGB and it fixed the washed out color issue when exporting.
Here's what was recommended:
- Quit Camtasia
- Go to your Mac's System Preferences>Displays
- Go to Color
- Choose sRGB for each monitor you have
- Export the video from Camtasia as usual (you may need to restart your machine)