What if I want to make my prototype into something I can reproduce - for example - are all future versions of my project dependant on having an Arduino attached?
If you don't need the USB port, all you really need to replicate your Arduino project is the ATmega chip and the crystal with it's 2 capacitors. There's instructions on the playground about how the Arduino IO lines correspond to the ATmega pins so you can easily wire up the project on perfboard as a standalone.
But what do you mean by port your project to EEPROM?