It turns out that you can use SSH in your EC2 instance and manually install ImageMagick, the caveat is that manual changes will not be saved if there are updates to the instance itself. The best way to do this is to create a .ebextensions folder and add a configuration file. Something like this:
packages: yum: ImageMagick-devel: []
Also, your .ebextensions should not be in your gitignore.
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