The term "media", and there are many types in the industry, is often misused. Depending on type, media will remove rust, which is one of its purposes. To be more specific, sand can warp panels when done by the incompetent. It wastes a great deal of material to strip body panels with sand; that is why other media is chosen.
Warping from media has nothing to do heat, yet the uneducated perpetuate this myth. Even some blasters think heat causes warpage until the basics of kinetic forces are explained. Stripping body skeletons and structures using more aggressive media will not cause damage.
Unless completely and thoroughly neutralized, soda will leave a residue that can cause paint failure. Which is why most have replaced it with other types of safe media like plastic, walnut and glass which do not warp panels or cause adhesion issues.
Every cavity, seam and pinchweld will have to be coated internally whether media blasted or dipped. Since that company in the link does not offer e-coat or any other coating service, the owner will have to take it from where the stripper left off. The decklid and hood can lose their NVH (Noise, Vibration, Harshness) when chemically stripped and dipped. Unless they are de-skinned, the NVH cannot be replaced on all parts of the hood, and none on the decklid.
The dipping company mentioned does good job of misleading people that media blasting is bad. I never had a problem or failure from blasting in 30 years. Their secret process is electrolysis. Any person can do small parts at home or the entire car if a tank big enough is available. The company also states they are not using acid, so there should be no weeping issues.
Media is a pain to get out, but so is the 40 years of sand, crud and debris in the rockers even before blasting. Whatever method chosen, there are areas that become thin from corrosion. Bottoms of fenders may look solid after stripping, but the area behind the brace is notorious for rot even on western cars. I just cut out the lower fender braces on a virtually rot and rust free LOS car because I knew what was behind them. Rear bottoms of quarters can do the same and unless you inspect below the trunk pan extension, you may not see it. Any reinforcement in an area prone to rot should be removed, addressed and reinstalled. Rear wheelwell lips have sealant that makes them rot. If you can epoxy the car on a rotisserie it is better. Epoxy can be reduced and the car spun so it flows into seams.
The photos don’t give the appearance of severe corrosion. Blasting would be suitable. Doubtful you will be driving this car like some do. Done correctly, the car will outlive you and no rot should appear, especially if a non-driving, trailer queen. My car that is actually driven in the rain, left outside sometimes and sees a hose is not failing after a restoration done 30K miles and 10 years ago.