Expose SDRAM as a USB 3 mass storage device
Ok, I can disregard the sanity of this project. It is insane, by the way, with little or no practical value beyond "doing it"-- but that never stopped me before and it shouldn't stop you.

In my opinion, you need several things:  A CPU, an FPGA, some SDRAM, and a USB interface.  Cypress makes the EX USB FX3 that does 2 of the 4 things.  It has an ARM 9 CPU and USB 3.0 interface.  What it doesn't have is an SDRAM interface-- which is why you want an FPGA.  The FPGA does both the SDRAM interface as well as the high-speed data interface to the USB3 logic.  

What you absolutely do NOT want is for the CPU to do the bulk of the data transfer!  A 100 MHz ARM 9 isn't going to be able to handle that kind of data throughput.  For that matter, just about any 2 GHz CPU isn't going to be able to handle that amount of data either.  The ARM9 is just there for the housekeeping, while the FPGA does the heavy-lifting.  

The ideal FPGA for this project is a Xilinx Spartan-6.  Relatively low-cost, easy to program, and has built-in hard cores for the DDR2 SDRAM interface.