Big positive news!
I got Aperture back, upgraded, and working fine under Mavericks.
Here's how I did it (from the Apple Help discussion boards):
1. Check appstore purchases to ensure Aperture is there.
2. Log-out of the AppStore
3. Move your own Aperture 3.5.1 to the trash - do not delete.
4. Open App Store and go to purchases.
5. Aperture should now show an install button. Press the install button.
6. Aperture 3.6 should now install.
Check it works, then empty the trashed copy.
Job done !