If you have picked up a wild yeast from the barrel I think that even maltodextrin or lactose will eventually ferment back out.
^ I would assume this is true and that you have some wild yeast in your BW.
I'm not completely convinced, however, because of how fast fermentation took off. You might have just restarted an incomplete fermentation when you racked OR there could have been residual sacch. in the barrel from the first beer.
Initially assume its wild yeast. You can cheat time a bit by "back-sweetening" immediately before serving the beer. Push a few gallons into a spare keg, and add a bit of simple syrup made with maltodextrin or lactose (MD if you want more fullness/body, lactose if you want the beer to taste more sweet). I would start with a small amount and dose to taste.
If you want to determine if the barrel fermentation was sacch or wild yeast, just leave this concoction alone for a few months. If it dries up again, its wild yeast. If not, repeat with the rest of the batch.
(If it were me, and you had wild yeast going on, I would transfer 2.5 gal into a keg, add 2.5 gal fruit puree, and wait a year. Serve for special occasions.)