I'm in a planning stages for June. Since I didn't apply for the lottery, I was thinking about starting at Horseshoe meadow and approach from Upper Crabtree Lake via Discovery pinnacle. due to time constraint, I am wondering if it is reasonable to do that section in one day. Or should I take a chance and try to get a walk in permit?

day 1 Horseshoe meadow to high lake
day 2 high lake to Blue sky lake
day 3 blue sky lake to Upper Crabtree Lake
day 4 UCL to whitney and portal

thanks for any input.