score:3
None of them. Many huts close before the end of season and start later the beginning. There is no need to spend time in huts but they are convenient for hot drinks and food and water if you don't want to lift it up whole. The end and the beginning of seasons are not just random days. Beginning get delayed sometimes because trails are blocked by snow.
And beginning of July is not really crowded.I hiked in July several times of total 9. Most crowded is the end of August. I stayed in the hut only first time.