Understanding ROM/RAM in ARM MCUs
The RAM on the Raspberry Pi is off the CPU. On the original models this was in a package-on-package - the newer models have it mounted underneath the CPU, on the other side of the board.

You may well find that you could extend the SAM3X8E in the same way - most MCUs have an external memory interface for this sort of thing - search the datasheet for EMIF.

The reason you can't find the Raspberry Pi's ROM size is that it has a small binary blob on the CPU that then supports boot from flash - again external, and in the form of a micro SD card.

Oh, and as to why the Raspberry Pi uses the CPU it does? Eben Upton works for Broadcom...