I wouldn’t characterize the New Testament descriptions of the risen Jesus as fuzzy. They are very concrete in their details. Yes, Mary doesn’t recognize Jesus at first, but then she does. The two disciples on the road to Emmaus (Luke 24) also don’t recognize Jesus at first. Their experience was analogous to meeting someone you last saw as a child 20 years ago. Many historians have argued that this has the ring of eyewitness authenticity. If you were making up a story about the Resurrection, would you have imagined that Jesus was altered enough to not be identified immediately but not so much that he couldn’t be recognized after a few moments? As for Mark’s gospel, yes, it ends very abruptly without getting to the Resurrection, but most scholars believe that the last part of the book or scroll was lost to us.
Skeptics should consider another surprising aspect of these accounts. Mary Magdalene is named as the first eyewitness of the risen Christ, and other women are mentioned as the earliest eyewitnesses in the other gospels, too. This was a time in which the testimony of women was not admissible evidence in courts because of their low social status. The early pagan critics of Christianity latched on to this and dismissed the Resurrection as the word of “hysterical females.” If the gospel writers were inventing these narratives, they would never have put women in them. So they didn’t invent them.
The Christian Church is pretty much inexplicable if we don’t believe in a physical resurrection. N.T. Wright has argued in “The Resurrection of the Son of God” that it is difficult to come up with any historically plausible alternate explanation for the birth of the Christian movement.
Read it all.