I may be wrong here, but essentially you have the same chip as in the UNO etc. The newer P variant has been developed with lower power requirements - picopower. Your device is packaged as the 28-pin version - so you loose a few pins over the 32-pin. A quick look at the datasheet says there's one less pair of VCC & GND pins and you don't have ADC6 & ADC7.
I think you can still load in a standard bootloader using AVRDUDE. I don't know if you can do this via the IDE as the device signatures won't match - as you suspected. I think you can use AVRDUDE from the command line and specify the correct chip so that the signatures match.
I'm guessing that once you have a standard bootloader installed in the 328, then you should be able to program it as if it were an UNO via the IDE. Just remember you don't have ADC6 & ADC7.