So, I had my second round off dealing with this issue last night. Go to leave work, turn key, hit starter, everything blinks off. Did some diagnosing and turns out the battery was drained. So, got it charging, didn't wait long enough between charging and try to start, and sure enough I welded my starter relay closed. So, I had a quick discussion with a local BMW mechanic, and he gave me a good run-down of how to un-weld a starter relay.
Un-hook the battery positive and get it fully charged.
Make sure you're in Neutral.
Reconnect the battery to the bike (and listen to your starter keep going, and going, and going)
Turn the key, and push the ignition to get the fuel system running.
The bike should start up, and the starter relay should un-weld. The previously mentioned 'light tapping' may be required is some cases to get it to un-stick.
My apologies if I'm re-posting 'common knowledge', but in my (admittedly hurried) forum searching yesterday afternoon I couldn't find the answer I was looking for. Hopefully this is helpful to someone down the road.
As an aside, Duncan, at Duncan's Beemers in Maynard, MA, is a good egg.