Well, after doing extensive digging, I came across this tutorial:
Show/Create AlertDialog with multiple choices in android
It resolves the issue of recalling previous selections in the checkbox AlertDialog by utilizing a boolean array. It needed only minor tweaking to make it work perfectly for my purpose.
In the event that the aforementioned page should become unavailable in the future, here is the code from the referenced tutorial:
MainActivity.java
activity_main.xml