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I found the solution while typing this. Config information was being stored in C:\Users\NAME\.EjsConsole.txt, which stores the JVM flags entered in the Advanced Options tab. I had to modify the flags to make EJS stop crashing on launch.
I'm going to leave this here, because I think it would be a good idea if this fact were added to the EJS documentation somewhere. I lost more than 3 hour to trying to fix this.