The cache partition isn't big enough for full rom installs unfortunately. All stock roms from Samsung/Verizon are indeed signed which is how the bootloader knows to allow them to boot. If it reads something with an incorrect signature, that leads you to that error screen about unauthorized software and needing to go to Verizon to fix it. So the only way to do so is to either figure out what that signature is (next to impossible), or find someway around it.
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Current Devices: Nexus 5, Asus TF700, Google Glass, (2013) LTE Nexus 7, Logitech Revue, Chromecast
Retired: Samsung Fascinate, Droid Charge, Galaxy Nexus, (2012) WiFi Nexus 7, Nexus 4