Umbilicoplasty or Tummy Tuck for Frowning Belly Button?

What you are referring to is similar to what was performed for your breasts. It involves removing skin and then suturing the resulting skin to the umbilicus. Not an ideal procedure and will not resolve the problem
You need to see a board certified plastic surgeon to see if you are a candidate for a tummy tuck as it appears that the majority of the loose skin you have is around and above the umbilicus.

Thank you for your question and sharing your photo.  I would recommend that you consider a tummy tuck as it will help reduce the excess skin that is above the belly button and help you tailor the shape the abdomen.  If you are strictly looking for a less aggressive approach, you will only be able to address a mild/moderate amount of skin laxity around the belly button.  

Belly Button surgery (umbilicoplasty) by itself only takes care of stretch marks and loose skin in the immediate area (few inches) of the belly button. In your case it is probably a good option but an exam would be required first to confirm this. Choose your plastic surgeon wisely for this procedure - see below link.