Avrdude and 328p-au

From a programming standpoint, an ATmega328P-AU is identical to an ATmega328P-PU, only the packaging is different (use m328p for either in AVRDUDE). The ATmega328-AU or ATmega328-PU differ in their signature bytes, so use "m328" for them (I'm not entirely clear from your post which chip you have.)