Unless AZ is radically different from the rest of the country, which could be, high school students need to have a certain number of credits to graduate, and a certain range of courses to satisfy requirements. The students can take higher weighted courses, which would be more difficult, and earn a larger number of credits. The minimum requirements are usually: 4 years of language arts, 3 years of social studies to include at least one year of American history and government, 4 years of physical education, and a three year sequence in at least one core academic discipline (math, science, foreign language), all on-level or higher. All other credits may be accumulated using a combination of electives at the discretion of the student. It's possible to graduate with more credits than one needs, and in fact this is quite common.

One period, even one period per day, can be written off as a study hall. It happens all the time. Students have schedules that include study halls so they may go to school-sponsored club meetings, go to the school library, go to a help session with a teacher, or even do their homework. Some schools will allow off-campus time for students during study hall &/or lunch, as long as they have express written consent of the parents and get back on time for their next class or their bus. One doesn't get academic credit for a study hall, though one can't leave the school without permission. Having regular study halls needn't interfere with accumulation of credits, and need never require summer school unless the student fails a course he's taking already.

A school day equals a certain portion of the day, which is why early dismissal days and late starting days (usually for snow and ice here in the Northeast) still count as school days. A day shortened by as much as two hours still counts, though schools don't like to have too many of them because it cuts into instructional time. So an absence from the school grounds for the length of a study hall doesn't constitute an absence from school in the legal sense, and they don't count up the hours to get the equivalent of a school day. For a student to be counted absent for a day, the hours must all be on the same day.

You haven't mentioned whether the release-time religious instruction you object to is every day, or if it's once a week, or if it's once a month, nor have you mentioned how long the instruction period is. If, as I suspect, it's once a month for an hour, my daughter's monthly trips to the orthodontist take more time than that, but she's still considered to have been in school for a full day that day. Make-up work is her responsibility, the same as if she's released early for a band performance or a rifle match. I doubt that release time religious instruction would be any different.

LDS students aren't receiving preferential treatment as long as this is offered to students of other religious faiths, and as long as their make-up work is treated the same as any other extracurricular activity's requirement.

People misunderstand the court rulings on the topic of religion and the public schools. The object was not to prevent people from practicing their religion or to prevent them from learning about their religion, but to prevent a religion from being practiced upon students whose families don't espouse it, and to prevent public money from being spent to support or endorse any particular religion or group of religions to the detriment of others. If parents seek to give their children additional work to do to study their religion, and it doesn't require an expenditure on the part of the public, that is well within the established body of law.