My reference for code 312 says it's a missing knock enrichment signal from the ignition module. Yes, a wiring/connection problem between the LH module and EZK module would have to be a consideration. Because you've just replaced the knock sensor I would be more suspicious of the knock sensor itself and the wiring to the knock sensor. Last time I heard of this code it turned out the plug on the knock sensor was accidentally left disconnected.

If you've double checked and cleaned up the wiring then I would say you'd have to suspect a bad knock sensor. You'd need a scope to check for the correct output signal, so it might be simplest to just test yours in another vehicle. What made you swap out the original one? Be sure not to over-torque the things (just a light 10-14 ft-lbs with a little thread locker) or you might damage it or cause it to become over-sensitive.