Is it possible for a V-qualified SSG(P) to be reassigned from Germany to the 173rd in Italy?

Anything is possible, need to start burning up the phone to assignments, of course you realize the higher the rank, the few positions available. Drive on!

Best bet would probably be to start with calling Branch, and seeing if you there's an open slot for you. You might also have better luck if you can convince your 1SG to call.