RS485 noise problems: signal ground / common ground / isolation?
I'm guessing that the pulsed current draw on the +12v supply is what is putting the noise into the RS-485 signals.  For debugging purposes, try disconnecting the LEDs.  If your noise issues go away then you know that it's that pulsed 1 amp current.  Assuming that's the case, then your job will be to reduce the current spikes on the +12v wire (which are also on the GND wire).  A filter using an inductor+large_cap would help.  Using a different cable where the power is isolated from the data could help too.