OK, just tried it again.
Did a clean removal of all other AV, and Avast again. I turned off Windows Defender in every single page that there was. I did a clean install of Avast IS.
Same problem, no luck.
Even Windows Defender settings recognises that Avast Antivirus is installed, and it allows me to run Avast from there, but again closes down within seconds.
So no solution, for a problem that shouldn't happen, to BitDefender I think?