Remember rocker panels are structural and fourteen gauge I believe. You have type three rust. That is the most serious variation of rusting we see. All the metal in the vicinity may be just reduced to iron oxide on some cars. A screwdriver penatrates it easily.

You have to probe around pretty seriously to locate where the really intact metal starts again. On the vertical surfaces it is pretty obvious. Sometimes you get a suprise and sometimes not on the more horizontal areas.

Can you cure of stop serious rusting? Generally not practical. But you can restore the integrity where needed and soak the areas with an oil grease mixture.

Nothing really stops the rust advancing but that type of petroleum application really reduces the rate of it more than substantially. Does a better job of blocking the oxygen from the metal than anything else I know of.
So the rate of oxidation in the future is seriously reduced by it.

Americans from the bible belt south probably have no ideal of what serious rust can look like up here in Canada. I hate using the anology of cancer but it is simular. You either have it in a spot and it is repairable. Or it is pretty well rampent throughout the lower body.

You are also lucky to find a person to work on it. Local body shops here on the east coast of Canada in general will not touch serious rust anymore. It amounts to restoration work to do it properly. It may be cheaper and better in some cases to get a car from the south of the states and swap things into it. Then totally rustproof it by the method I suggest. Thats especially if the car is to winter driven at all to preserve it. We even have a hydralic grease gun designed to spray a purchased product called grease and graphite into most areas. Air pressure drives a pump that produces 3,500 pounds of hydralic pressure to spray the grease. Inside closed rocker panels etc.