First of all, where in Washington are you headed? There is a pretty active blacksmithing community here, I can help you get in touch.

Second, I believe the word you are looking for is "carburizing" .

This manufacturing process can be characterized by the following key points: It is applied to low-carbon workpieces; workpieces are in contact with a high-carbon gas, liquid or solid; it produces a hard workpiece surface; workpiece cores largely retain their toughness and ductility; and it produces case hardness depths of up to 0.25 inches (6.4 mm). In some cases it serves as a remedy for undesired decarburization that happened earlier in a manufacturing process.
https://en.wikipedia.org/wiki/Carburizing

This is also called "case hardening". What material are you trying to harden? The stainless foil only protects the material from O2, which can be a problem trying to case harden steel (well strictly iron or mild steel, anything with less than .4 C). You are not going to migrate anything from the foil.

Traditionally, you prepped a piece of iron to case harden by packing it in a sealed environment with some kind of carbon rich medium, ground bone and cow dung we commonly used. This was then heated to about 1500 F for long periods, days often. My relevant text is packed, but if memory serves you get penetration of something on the order of 1/10th of MM per hour of carbon migration in 1 inch square stock. Once the material is carbon saturated, you then harden as normal.

It's true that you want a reducing flame for the HT process (O2 will leach your carbon back out of the steel quite fast) but steel when sealed up doesn't care how it's heated.

Today, when this is done they use big induction coils in a sealed chamber of CO2. No matter what, it takes hours at temp to get results.

Geoff