If LN is off-chain, and the transactions are all contracts that aren't published by miners... is it still redundant?
"It depends": you'll be responsible for your own backups, just like you're now responsible for backing up your private keys. It's up to you to make redundant backups.
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.
There aren't that many miners. Stand-alone mining is very rare nowadays, and pool miners don't even need their own copy of the blockchain. There are about
10,000+ full nodes, and many people like me who run Bitcoin Core to keep a full copy of the blockchain. But that's not going to help anyone who lost their own private keys.
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.
There is no central system between those two parties.
Doesn't that simply create an exploitable hole that allows for hacks and cheats that would just weaken bitcoin overall?
No. Bitcoin works with or without LN.