Several considerations here . . .
Building inspector - what they don't know won't hurt you. You are repairing a small, existing structure. A lot depends on the attitude of your building inspector and tax assessor. If you get a permit, that will alert the assessor that something has changed, and they'll come say hello.
If the building inspector is a retired East German border guard and the assessor is his even more evil twin brother, I'd do the repairs on a weekend because they don't work then. I think I'd also take a look at code (online, where you are anonymous) and see what the maximum size of a building can be before a permit is required. 12 by 16 is 192 sf, if the permit requirement kicks in at 200 sf+, go have a good time. If it is less than that (your building is required to have a permit), think about fixing it on weekends, especially holiday weekends because you get an extra day to do the work quietly.
We happen to be exceptionally lucky in this regard. Our building inspector tells you how you can do something, not why you can't. I built a 4,500 sf hangar, he said "It's a BARN, right? Hangars can't be more than 2,500 sf, you built a BARN, right?" "Umm, yeah, you know, you're right, it IS a barn!" (Our maximum size here for no permit is 100 sf unless it is an agricultural structure.)
As to your building itself, after you have successfully avoided any "Imperial entanglements", the idea of carefully jacking up the corner after reinforcing it and then lowering it carefully onto a proper foundation sounds like a good approach. This isn't rocket science. If you think it through and ask for help and advice (as in this group ;-) I think you'll do fine.
One thing you might want to consider is buying a 20 foot shipping container and replacing the wood building entirely. You're in WV so I don't think the termite problem is too bad, here in FL, invasive Formosan termites would eat that building in one summer as an appetizer and then start on your house.
Best Regards,
Mike/Florida