BMW R1200GS (2008 model) starter motor overhaul. Reason for removal

In this video you will hear the bike start up and note the hesitancy before it cranks over properly. The battery is fully charged and the bike has always behaved this way since I acquired it almost 2 years ago. I don't know the age of the battery but, before buying a new one, it seemed to make sense to give the starter motor an overhaul. If this overhaul makes no difference, then perhaps time for a new battery.