My dad has a 55 chevy. Same problem as yours only maybe not so bad in some places and worse in others. He basically replaced the firewall and rebuilt the bracing, drains etc. If I remember correctly, he opened up the cowl and treated the rust inside completely, which is the only real answer. Take pics, measurements and make templates. Split the work into smaller pieces and when you get tired or frustrated, work on something else.
He was supposed to do a 1yr clean up and go; ended up with new partial floorpan, trunk floor patch, quarter panel, inner and outer rockers, both rear wheel houses, new brace for the rear shocks and plenty more. It took 5yrs. Best info aside from the above is get yourself a rotisserie....it woulda saved our backs and been much much faster, and you can sell it when you're dont and recoup most of the money