1) BRAT type rides - Most people just use a seat wedge. I use a seat post rack with a trunk bag on it so I can carry bad weather clothes and everything else I might need.
2) Weekend overnighter at a motel - I have done this with a rear rack and small panniers like you said. That will be plenty of space for moteling it. You don't really need fenders.
3) 2-3 days fully loaded - you might need a different bike unless you can pack really light. I think your front fork is carbon and I don't think you are supposed to attach racks to those (unless it is specifically made for it, which I don't think yours is). The picture I saw of a Trek 1200 doesn't have eyelets on it so maybe you have a different fork.
4) Personally, I don't like trailers but that is definitely an option for you and your bike to do a fully loaded trip.