That sucks that the Madison hut was closed, especially in the cooler weather! they usually have some decent soup there! No wonder your legs were tired, thats alot of elev gain! you weren't missing anything on the valley way trail, it's boring but probably would have been quicker!
The elevation gain did take away today's hike though. I was supposed to hike up Mt. Cardigan with my wife today and her friends but my legs were way painful to do it! My wife and I have done it before but never in fall and the colors are now peak. She and her friends went but I stayed back to recover from my adventure. It is her first hike without me in ten years! I still though have absolutely no regrets and am happy that I capitalized on Adams and Madison. Mt. Adams and Madison clearly ROCK!! and are some of finest summits in the each. I just wish her trip was next week.
This is one of the best loops in the Whites.
One small correction: you'd have had sunlight on the summit (of Adams anyway) until about 7:00 :)