Adam, LOL. You arrived in the U.S. safely and in good form, I see. The thing about cheese with a dish like this is that it can easily overpower the subtle and very simple flavours. By all means, add it if one wishes. It's just a different dish. Also, cheese covers over the tastes of seafood. But if that's what one likes, then great. Just don't pay too much for the cheese or the seafood.