For me, it's not the content or level of detail / effects but how the game is presented, again.
The feeling of rushing is because player is moving in too linear way. I know you have played this a million times and know what to do but as someone first laying his eyes on the game world you created I feel like I want to see more and that I have no idea where to go. I want to wander and explore. But the player on video snaps on the tracks and does stuff without stopping to think and the viewer can't relate to that.
Honestly when I said "gameplay material" I was thinking about your "feature set complete" statement and assumed you had some of this you wanted to show. You could do it in a way that supports building the atmosphere. For example first make camera drives in the pouring rain and then show small scene of fireplace being lit bringing warmth and juxtaposing the elements.
I like the end where you zoom back to the lighthouse. You could depict it from frog perspective to give it a little mystery and intimidation if that's your intention.
I feel like there's no real need to wait for later production stage with what you got, I'd be interested to seeing another version of the trailer with a bit more cinematic sections mixed in. But whenever you decide to go for it remember to slow down in the gameplay and do non-linear editing to break up the pace and bring variance in the trailer. Could definitely take more text to give the viewer something to chew on while enjoying the view.