Update: Thanks to a tip off from @MrAbe101 I found out that teachers can apply for a free educational account here. This extends the video length to three minutes and allows you to create 50 videos with your class in a six month period. I applied and was immediately accepted to the upgraded account. I created the video on Casablanca, below, as an example of how to use the extended time.
The Truman Show - Cul. Context
The Truman Show - Cul. Context (2)