I am so glad I decided to bring my project to this forum for assistance! You folks have offered such thorough advice and insight that I feel much better equipped to tackle similar projects in the future. As Nat pointed out, this style of project is a growing trend in my field and I hope VideoPad will continue to evolve with that in mind. A larger range of grid options would certainly have made this a less complicated task.
In the end, I created three separate videos. One for the leftmost 6 boxes, one for the middle six and another for the rightmost 6 boxes. Six at a time seemed to be the most my computer could handle without boxes flickering and disappearing. It was then fairly simple to layer those 3 videos on top of each other. The finished product looks quite professional with only the slightest imperfection in the grid layout.
Thanks again for all of your help. This will be a very special part of our school's virtual graduation ceremony!