The Sprint variant of the 5s is the iPhine6,1. Also, sorry to hear about the problems you were having. For me, beta 5 has been the least buggy, but that's just me. Also, you don't have to put the device into DFU mode to restore to 7.1.2. You just have to download the IPSW and do shift+restore (or cmd+restore on OS X) and navigate to the IPSW to downgrade.
-Anthony