I think this is a no-win challenge in Creo. And you are right, the provided model is less than stellar.
The only thing that will work is to rebuilt the entire surface with sections and reference points for either a blend or boundary blend. You can use exisiting surface to characterize the new surface, but in general, I would try to make it independent. In IDD, separate out all the affected surfaces so they can easily be removed for the solidify process. Then determine the best way to rebuild the existing and missing geometry.
Blue... what is this feature?