Rob, from the sounds of things, you got it covered. Chemical stripping or heat stripping from a rough surface would be very expensive and time consuming. Water blasting might get some off, but probably not all of it. Sand or similar blasting would be the way to go. This will be expensive also and you will probably have to have some kind of staging for working on the higher levels.
I could not give you cost comparisons since there are so many variables but the actual staining will be the easiest and cheapest part, from the sound of things.