This seems extremely odd. It is not the charger. I would be careful. Like NDM said I would leave the bike alone until you get the battery replaced. Although rare, your bike might have the symptom that was one of the reasons they are doing the battery replacement. Make sure you have your appointment to send your bike to the factory as soon as possible.
Although as a last resort, try pressing both buttons at the same time on the BMS behind the front rubber cover. But use something that isn't metal to press them and be careful, one is slightly hidden behind the cover. That might fix it but perhaps unlikely. Just get it to the dealer if this doesn't work.
6.2v is unlikely. I would guess the cell would be close to wanting to burst into flames vs be at that state of charge. Just in case that is an accurate reading, seriously get the bike to the dealer right away and definitely don't plug it in anymore just in case.
Ok just saw your reply to NDM while I was typing this. I have more than a dozen friends, Tony Helms, Brian Rice, Jeremiah Johnson who are on this forum, and many more on the facebook owners group that have a 2013 Zero and got a 2016 Zero recently so they wouldn't be without a bike during the battery replacement waiting period, and will probably sell the 2013 once it gets back with a new battery at a higher price (thank you Zero for their sake!) due to the increased range.
I have had 2 Zero's as well (2012 and 2015) and understand, I would never want to have to ride a gas motorcycle again either. A 3 year difference is a good time to appreciate new features. So I would suggest upgrading to a 2016 as soon as you can, and get the 2013 in for the battery replacement. My buddy Brandon just ordered a 2016 Zero 2 1/2 weeks ago and had it delivered 5 days after he ordered it. Hopefully you can get yours just as fast so you are not without a bike to ride.
Brandon has upgraded each year and has said it's totally worth it. He has owned a 2010, 2011, 2012, 2013, 2014, 2015 and now a 2016 SR also! Awesome Brando! So trust me you will appreciate the advancements from the 2013 to 2016 a lot!