I'd rather not bother with Kies if I can avoid it.
Flashed the update file from Sammobile. Thanks.
Flashing ICS seems to have killed root, which I guess makes sense since everything got wiped. Flashed CWM recovery via Odin, but flashing root from within CWM doesn't seem to work on ICS (it worked fine on my GT running HC).
Edit: Need a different root file for ICS. Can get it here:
How to Root ICS on Galaxy Tab 10.1! | Galaxy Tab Hacks!