First - something doesn't quite add up as you've described
When in a flashback compiz session here & the profile is 'unity' then I get a unity launcher & no panel indicators, you don't seem to have that?
Anyway, the only way I found to switch back to Default profile other than doing in ccsm (though again here the switch back in ccsm sticks thru a log out/in
In ~/.local/share there are some files, delete -
and for good measure -
Then do a restart (because I had nothing else used sudo reboot in a terminal