I got my MHL adapter from monoprice and it seems to work without having to reboot my phone. Are you sure that's the native resolution of your TV? I've never heard of that resolution for a TV (it's super close to a 16:9 aspect ratio but not all the way there) and I'm not sure what HD ready would mean...
Otherwise it might mean that your phone is putting out HDCP encryption and your "HD ready" TV doesn't support HDCP encryption. If your phone is rooted, you might be able to turn off HDCP...under developer options (HDCP checking). I'm not sure exactly what that setting does, but it might help if you're rooted.