If LaRoche comes back, I think the Yankees might be one of the better fits out there for Morse (for most hitters, really, but especially for Morse). The Yanks have 3 lefty hitting outfielders already and their best hitter, Cano, is also a lefty. Morse would fit well with his right handed power. The short porch in right field would also help him put up big numbers.
If LaRoche does come back (at this point the Nats are probably his best ticket to a WS ring), then the market for Morse is small. I'm not sure if the M's would still want him, but he can play LF so there may still be some interest there. Yankees, O's, Phillies and maybe Rays are the spots I could see.
Yanks would have to offer something from the MLB squad since their minor system is quite bereft. O's, well, I just don't see a fit unless the Nats really want to take a flier on one of the washouts like Matusz. Phillies, just eff no.
I want it to be the M's because I really want Carter Capps on the Nats. The Rays would also fit well but they notoriously don't trade big pieces to get MLB guys. Almost every trade they make, the Rays become the winner of, and yes that is a mindfact.