I don't know about the dual soundcard idea, but you should be able to back-up from your dat deck > digital out > digital in to your 722, and then transfer the resulting file from the 722 to your pc.
A little bit extra time as you need to transfer from the 722 to the pc, but a file transfer will only take minutes compared to real-time. Then you can also do real-time transfers via your soundcard at the same time.