The stuff that fell out, clearing your beer the first time, is going to fall out again fairly quickly. Even quicker, if it's cold. Keg it now, chill it, and the cold will slow down oxidation quite a bit.
At least you weren't using a carboy that shattered, sending beer and glass all over. Plus, having fresh IPA on tap is a joy. So much of a joy I bet it won't be around long enough to oxidize