I do not think the Mount Washington is the best idea for you, I simply can not see the romantic moment that you are looking for. I think it can ba a bit honky tonk at times.
Don't get me wrong there is defiantely a good time to be had on the Mt Washington, but not for this proposal.
One of my favorite places on the Lake is the boat house in Senter Cove / Winward Harbor. I guess you would need a friend for that one. I have seen weddinngs there and the place is beautiful.
The grounds at Churchs Landing in Meredith really are lovely. I think that would be good if you need a photographer present. Quite frankly, I would avoid the photogropher and be out on the water, if you want a beautiful sunset perhaps off Long Island on the western side facing Braun Bay. Just you, her, the Lady of the Lakes, some nice champagne and strawberries....oh I almost forgot a diamond worth 4 months salary....
Good Luck