If LN is off-chain, and the transactions are all contracts that aren't published by miners... is it still redundant? Bitcoin is infallible only because you have redundancy between millions of miners who can confirm transactions because they all match up with everyone's ledgers.
But if LN is not mined, then it stands to reason that there's some kind of central system or some kind of system where the transactions are only in existence between two parties.
Yes, that's how it works.
It's just between two parties. There are no nodes that store all the commitment transactions between peers.
Doesn't that simply create an exploitable hole that allows for hacks and cheats that would just weaken bitcoin overall?
No.
If you try to cheat the system, you'll be punished by losing your funds in the channel.
Lightning network transactions persist as channel states, if you try to publish an old channel state (which won't be mined because it's timelocked) then your counterparty will publish a transaction that takes your funds in the channel.
Read the lightning network whitepaper
It's documented there.