I've run into this issue as well a while back, if I recall correctly, the synchronous FIFO would only work on channel A, so if you're for some reason bound to using JTAG via Port A as well: no such fun.
Also, you might consider the isochronous option (which you can't do with the FT2232), if you have large amounts of data to stream which you can't buffer (like video), that's were the Cypress FX3 (or legacy FX2) are/were popular, but they again require careful programming. Thus, not exactly plug&play, but there are many reference projects to steal from.