Can my middle vault be reconstructed?

Thank you for your question. It is difficult to tell exactly what is causing the irregularity for your pictures, but a rhinoplasty to improve the appearance would likely be feasible. I recommend consultation with a board-certified facial plastic surgeon for an in-person examination and to discuss aesthetic goals. At our practice, we use imaging software to ensure we are on the same page. Given your history of the previous septoplasty, it may be necessary to harvest additional cartilage from your ear or rib for grafting. Best of luck!

The included photographs are only front views(no profile) however based on your history, it is like that your cartilaginous dorsum(bridge) was dislocated from the bony dorsum(bridge) with the punch.
This created a depression where the cartilage bridge meets your nasal bone(as well as deviation as seen in the last photo).
Yes this can be fixed with an open rhinoplasty, giving proper visualization for inspection and repair with cartilage grafts and suspension and fixation of the bony/cartilaginous junction.
Let me know if you have additional questions