1. Replace it with a 2nd hand known working unit of exactly the same type out of a breaking car.
2. Same as above.
I 'might' be wrong, so forgive me in advance, but the amplifier in the logic 7 setup is 'just' the amplifier and it's 'fed' the audio signal via the MOST bus system in the car. There's no aftermarket replacement amplifiers which connect to the BMW MOST system/protocol, so you 'have' to buy a BMW unit and have it installed in order to have any audio capability.
If you are lucky, then once dried out the amplifier may work again, if not, there are places I think which can refurbish the oem Logic 7 amplifiers - not sure which places can in the USA though, I've only vaguely heard of a few places here in the UK.
As I say, if there is a new 'aftermarket' amplifier or indeed interface with RCA outputs which connects to the BMW MOST bus protocol, I've not heard of it so far... perhaps there is something ?