I don't understand the "I will be hiking with 9 other strangers unless I can get one more permit
You can count on getting a permit when you walk-in. Based on the unused permits
numbers, dates in May for overnight permits have NEVER filled up, except Memorial Day weekend.
You will likely be able to get one on May 1 when people who won lottery permits who haven't paid for them will lose them. Check online throughout the day on May 1
. But even then, go on the trip, walk into the Visitor Center and ask.
By the way, in May, there may not be a store, but there will definitely be snow. I doubt people will be using the trail past the cables at that date. Instead, they use crampons and climb the snow slope west of the switchbacks.