I would advise the OP to just move on to a replacement vehicle, as rust that is this extensive is equivalent to cancer that has begun to metastasize in a person’s body. (i.e.–You can remove a tumor in one place, only to find another tumor in another portion of the body a few months later, as a result of the metastasizing of the malignancy.) It might be possible to do a temporary repair in this one area, but–more than likely–there will soon be too little intact metal left to weld on.
And, what should concern the OP more than anything is the likelihood that this car will simply collapse in the event of a collision, rather than absorbing energy in order to protect its occupants. Severely rusted metal will not retain the “controlled” energy absorbtion of the original design.
As to, “A family member advised that I should contact Mazda and/or the better-business bureau as the rust seems extreme for its age”, there is no warranty coverage of any kind or even “good will” coverage on a vehicle that is ten years old. I would be extremely surprised if Mazda (or any other car company) was willing to give you repair assistance with a ten year old vehicle.
And, as to the BBB (better known as the Better FOR Business Bureau), you should save your time and effort. When Smart Money magazine conducted a study of the BBB a few years ago, they concluded that, “Few consumers are actually helped by the BBB”.
With a ten year old car, I have to seriously doubt that you have any recourse other than to replace this car with a newer one, and to remember to faithfully rinse the undercarriage of that replacement vehicle after every snow storm, in order to rid it of as much road salt residue as possible.
Sorry for the bad news.