I feel like you need to train your body for two separate things, to climb Denali in this style.
On the lower mountain, you need to be able to carry a very heavy load, maybe 50 pounds in the pack and 50 in your sled, but the total vertical gain per day isn’t large, you’ll climb 3000 feet at most. To train for this part, my hill climbs were usually only 3000′ of gain, but I always used 50 pounds or sometimes more in my backpack. Some people say you want to train your muscles specifically for the sled dragging, but I didn’t find that essential.
For summit day, you need to be able to gain 6000′, at high altitude, but maybe only 10 pounds on your back. Scott says in TFTNA that he can do that in 5 hours up and 2 hours down, but I think that’s incredibly fast, it took my group almost twice that. You won’t be limited by leg strength but by general aerobic fitness. The best way to train for a day like that is to go and spend a lot of hours continuously moving on a mountain.
So, I’d think one answer to your question would be to do one of your carries each week shorter and heavier and make one day lighter but longer.
I think I’d probably injure myself by trying to do two 7000-9000′ gain days each week with a heavy pack, but maybe fitter people can get away with that.
Hopefully Scott or Steve can give a better answer.