Can we configure the payment to use any secret of our choosing? Such that it could be generated months or years before the payment takes place? Provided the payer gets the hash of the secret at the time it is generated.
AFAIK you can use any secret you want. However, very likely you'll have to use a custom implementation (or manually enter the script) for your transaction(s), as LN software will generate secrets automatically.
I wonder however what would be the exact use case you have in mind. Atomic swap via LN maybe (you wrote about "exchange")? Yes, that should be definitively possible.