Glad you got it taken care of before it got Bad! Real bad.
Congrats on the home purchase. Sounds like you are on the beginning of the learning curve as far as home owning goes and learning fast. Few things can get more expensive than not immediately addressing a problem when it comes to water in the home.
As far as the remedy goes, if I understand it right, he ran plumbing across the attic to the new addition? Yikes! Maybe rerouting pex sometime in the future...
But in the meantime, I'm not sure I would rely on a heat tape for years for long.
If you kept the pex as close to the ceiling as possible, with 18" insulation above it ,and zero insulation between the ceiling and the pex, you would be better off. Heat loss through your ceiling is plenty for this, as long as you trap it with a blanket of insulation over the pex.