Re: Paneling over popcorn
If you install furring strips over the popcorn you'll probably be ok, however I'd be concerned with hanging MDF because it has no structural value of it's own and will sag soon after installation. If it were my project I'd skip the MDF and go with actual T&G wood, particularly in a wet location such as a bathroom, the MDF isn't likely going to hold up to the steam and moisture. If you go with wood, sc**** the ceiling and hang it perpendicular to the rafters.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!