Avoiding crowded times in southern Utah national parks and monuments

Frequent advice to avoid crowds when visiting national parks in the USA is to travel outside summer (example: (1), (2)). However, some parks have more visitors in May than in July or August. For example, in Canyonlands National Park, Natural Bridges National Monument, or Capitol Reef National Park, May is the busiest month of the year. Clearly, visiting in May is not necessarily effective in avoiding crowds in the Southwest². I suppose it's the climate motivating people to visit in May.

Is there any higher temporal resolution information to avoid crowds, specifically in southern Utah, in parks like Zion, Bryce Canyon, Canyonlands, Capitol Reef, Grand Staircase-Escalante¹? In other words, might specific weeks in April or May be much more crowded than others? Official visitor statistics are monthly. I thought of avoiding spring break, but apparently “spring” break is in February (!) or March. National park week was 21–29 April 2012, 20–28 April 2013, 19–27 April 2014, and 18–26 April 2015, so will presumably be 16–24 April 2016. Memorial day is in late May. Apparently, teaching at universities ends in June, the same for other public schools. So, I'm confused how May is the busiest month — I wonder who all those visitors are, considering that neither students nor families can visit for more than a long weekend, and there anyway aren't any long weekends in April and May except for Memorial Day. How can I find a 2–3 week period around April/May where one can expect the least crowds in southern Utah?

¹^{Of course, 6 parks is way too many for 3 weeks, but one reason to travel during a less crowded time is that one can hope to remain flexible and choose the specific park less than a year ahead.}

²^{I know this is a popular area, so asking for solitude is not realistic, but I suppose a park as large as Grand Staircase-Escalante should not always be as busy as central New York City, or at least not everywhere.}