I am fortunate that I live pretty close to Carolina Chem Strip. They do cars all the time and they did one I was hoping to be finished with and crushed a disc. I also have a friend that has been restoring cars for 36 years now. He has never advertised and does not have a web site does not need one has a waiting list always. He also uses Carolina Chem Strip.
The first place you go with any ground up restore is a frame shop to have what is left of the chassis put back as close to zero as possible.
What ever shop you use has to have a chassis JIG or they do not know what they are doing.
For a car as rusty as that one there will be at least 2,000 hours of labor plus all the materials and parts.
There is a shop near Atlanta that does only panel replacement and no body work. One of our members, that I will not call his name, had them do the panel replacement on his car which was inner fenders, cowl, floors, some frame, trunk, quarters, wheel houses pretty much the whole chassis. The car then went to a body shop that worked the metal fit the gaps and painted it. This car won best of show with over 1,000 mustangs entered this year. So that speaks highly of their work and they are not expensive either. They are Grave Robbers and I will have to get a link to their site.
https://www.graverobberssheetmetal.com/index.php/custom-frame-jigs
You take a bare dipped chassis to them to work from.
Now back to dipping,they use a combination of ovens and dipping to remove all paint, sealer and of course rust. After it is all clean they wash and then do phosphate coating that will prevent rust in a shop for months while panel work is done.
The car that I have has been sitting over 10 years now with just epoxy primer on if for now and no issues. You will not get bleeding from seams like some say the dipping does.
Your car has pop open gas but 73 side stripes. A 73 will not have red oxide primer but will be gray and not slop gray but gray epoxy primer. All 71 and some 72 will have red oxide you need to find original paint and primer to know for sure.
The cost to dip was around $2,100 but has probably gone up like everything else. What is left will be filled with pin holes but most of the car will require replacement for sure. Here is link to Carolina Chem Strip.
https://chem-strip.com/portfolio/
Someone said something about insulation in the hood on these cars. There is no insulation inside the hood. There is dabs of seam sealer between the inner and outer hood to keep it from vibrating. E-coat was also mentioned but E-coat will not get between the inner and outer hood stampings. There is not enough flow of material to get a coating inside. The tank is not all paint but about 80% water with 20% paint in suspension and the electrical charge pulls the paint out of the water onto the metal.
I would expect the restoration to cost well over $100,000 probably $150,000 for a true Concourse Restoration. It will take a minimum of a year and the painter will need to let the primed and body worked car sit for couple months to allow the primer and bondo to shrink before final blocking. Now please remember that Grave Robbers is not a body shop. Any bare metal will get epoxy primer but no body work will be done.
I know you say the car is sentimental to your family but you are going to end up with a mustang made in Taiwan. You would be way farther ahead to find a rust free California or desert car and move the VIN# and drive train. You are legally not allowed to do that but some people do. Would be better than repo sheet metal. I was an automotive product, process and tooling engineer for over 25 years so I know metal. The repo metal is much softer to all it to form easier so if you lean on a quarter panel you will probably put a big dent in it.
I picked up a totally rust free 1973 Grande from Arizona that will go to dip strip and then make a track days car. It was only $1,000 and was loaded with great options. Not even the battery box is rusty.
My friend with the restoration shop had done a camaro that all that remained from original car was the windshield frame, A posts and the part of the cowl with the VIN#. Every other piece was changed out. AMD in Atlanta did panel replacement and he did body work, paint and assembly.
Like me he has bad back so is stepping away from builds like that and going to lighter easier work.
So it might cost you some shipping to get the body to Carolina Chem Strip and then to Grave Robbers but you will save tens of thousands of dollars. You can probably get a little saving on the dip if you do only pieces you will be using and not pieces that will be tossed.
If you find all the parts you will save a 15% mark up by the shop usually. Grave Robbers buys so many panels they get them cheaper also. Some of the parts are not made so will have to be rebuilt. Not for the faint of heart.