The sort of off-chain processing I mentioned requires the wallets / holders to enter a special smart-contract (state-channels) that locks their tokens. Think of it as a having a tab at a bar where the barman keeps track of your orders and at some point may tell you the tab is closed and you don't have any credit left. In fact that very method was used recently in a festival here in the Netherlands (https://blog.loyalgarden.co/running-a-live-festival-on-crypt...)
Double-spends can only be securely verified once the transaction is processed on-chain but keeping track of nonces and signatures can be done with a secondary (off-chain) system which is easy to do with a limited population.
The Suntainers we built have WiFi and GSM included so that transactions can be relayed along the ground network.
