If the Internet goes down, the Amish community will be the only ones going about life as usual

perhaps trading bitcoins using paper wallets?
This would be possible if the miners continue running and part of the population still has an Internet connection. Without internet you need another network. Without a network you can do mining on paper and keep a printed copy of the blockchain, but transaction time would be very slow

Actually, the transaction time would still be 10 minutes. Difficulty will be adjusted down. It's always 10 minutes by definition.