The Lighthouses prevent the decks from getting too junked up by Sea Hag and make the Ghost Ship a lot less threatening. So I don't think the board is too "disgusting". His deck runs considerably smoother than yours because he removes all treasure from it. And once he gets one Grand Market then getting more is much easier.
Crossroads becomes a better draw card whenever you can remove treasure, have another village (FV), and have something to seed your hand with some green cards (here the Ghost Ship and cantrip property of Grand Market).
In general, getting more Lighthouses isn't necessarily the best way to guarantee protection, I'd rather have a deck with 2 Lighthouses that I can play each turn then one with six. I think the aggressive trashing of your opponent let him provide better Lighthouse protection. And of course there's a lot of shuffle randomness involved in this kind of thing as well.