That's insane. There are dedicated controller ICs that will do just that, properly.
But what is this mass storage about? You're talking about RAM but not permanent storage at all. Is this something to emulate a mass storage device but only RAM-based, maybe? (Which would explain why of-the-shelf controllers would not cut it.)
If so, then using some ARM SoC will be much easier than a FPGA, yes.
If this is a student project, then it sounds pretty ambitious. If it absolutely has to be a FPGA, then using a FX3 for implementing the USB side would make it much easier. But in that case, the FX3 would implement the mass storage USB device and would provide a FIFO interface to the FPGA, which would just handle read/write requests and implement the DDR controller. Still sounds like a lot of work.