Okay, I figured out the problem in case anyone else runs into it and needs help.
CWM will always not register the phone as the one you want, but TWRP does. So if you use another ROM that installs TWRP first (like say, SlimKat), you can then install Beanstalk from TWRP.
Device: Samsung Galaxy S 4G @1.2GHz
ROM: KitKat Beanstalk 4.4.225
Launcher: Nova Launcher