The 328 has a different device ID than the 328P. Either create a section in avrdude.conf for the 328, identical to the section for the 328P, except using the correct device ID, or use the -F switch on the avrdue command line like this;
avrdude -pm328p -cusbtiny -Ulock:w:0x0F:m -Uhfuse:w:0xDA:m -Ulfuse:w:0xFF:m -Uefuse:w:0x05:m -V -Uflash:w:ATmegaBOOT_168_atmega328.hex:i -u -F
Which will program the chip with the Arduino Duemilanove bootloader. Just change the "ATMegaBOOT_168_stmega328.hex" to the name of the file you want to use.