Cosmos for a local, ephemeral, permissioned blockchain?

We need to build a blockchain in an isolated setting (local area network without internet connection) where all participants are known ahead of time and they are largely mutually distrustful. I think that a permissioned blockchain is the best fit for this application. Does Cosmos support such a design? Or the mandatory (IIUC) PoS will prove to be a lot of overhead (both in terms of development & execution)?

Note that in principle one can emulate a permissioned blockchain with PoS by giving 1 untransferrable coin to each party (IIUC).

Yes. Tendermint supports this. POA. But what you are referring to is done on testnets.