Whelp, since Kewitt only suggested it in passing..

Yes, get an authenticator. Either buy an official keyfob or download the Android/iPhone app (which is free).

The 'account compromised because IP changed' thing is a v1.x feature they removed for v2.0 .. and then re-added because it was bloody effective. It might be annoying but with the rash of hackings it was a good first move.