Thanks for your helpful response - as expected, the signatures don't match when trying to burn the bootloader:
avrdude: Device signature = 0x1e9514 (probably m328)
avrdude: Expected signature for ATmega328P is 1E 95 0F
Double check chip, or use -F to override this check.
avrdude done. Thank you.
So it looks like there is no native support for the ATmega328 directly in the IDE as an available "Board" - I assumed there would be as I've done similar device level flashing on Attiny's like this before.
Wondering if I'll brick the IC if I override with -F......