A simple jumper from the arduino board's reset pin to the 1284p reset pin should fix that situation. Try that and let us know how it works.
You may have to also remove the reset pull-up resistor on the 1284p chip as there is already a reset pull-up on the arduino board and having two in parallel may be too low a resistance for the auto-reset pulse to pull the signal low on initiation of the DTR signal.
Still, got the error, "avrdude: stk500_getsync(): not in sync: resp=0x00".