The text is read clearly as "his sweat fell to the ground like [falling] drops of blood".

Compare "ta himatia autou egeneto stilbonta" 'his clothes became shining' (Mk 9:3), "to hudōr oinon gegenēmenon 'the water having become wine' (Jn 2:9).

http://tiny.cc/bostonreaders for a new translation of the New Testament (IRENT) [Note: continuously being updated].

Jesus of Nazareth is crucified in Jerusalem in circa 30 AD. As he draws his final breath, the entire earth goes dark for three hours, a violent earthquake shakes dead people awake in their graves, and rips the Temple veil down the middle. Jesus' body is taken down off the cross and placed in the tomb of Joseph of Arimethea, a member of the Sanhedrin, the Jewish governing body which the previous night had voted unanimously to execute Jesus. The tomb is sealed with a large stone and Roman guards placed in front of it. Three days later, a second great earthquake shakes Jerusalem, causing the dead who had been shaken awake in the first earthquake to now come out of their tombs to roam the streets of Jerusalem and reconnect with old acquaintances; an angel (or angels) comes and rolls away the great stone in front of the tomb, causing the soldiers to faint and testifies to one, several, or many women that Jesus' tomb is empty; that he had risen from the dead. Jesus later appears to the Eleven, and eight days (or forty days) later, ascends into heaven from a mountain in Bethany (or Galilee, or from the Upper Room in Jerusalem). The resurrection appearances of Jesus so emboldened the previously easily-frightened, doubting disciples that they now boldly preach the gospel of Jesus in the temple, Judea, and the world, dying martyrs deaths, refusing to recant their eyewitness testimony that they had seen the resurrected, walking/talking body of Jesus. These same disciples soon write the Gospels and several epistles that would soon become the New Testament of the Bible. The Gospel of Jesus spreads like wildfire, even though furiously persecuted by both the Jews and Romans, to become the dominant faith of the Western World for two thousand years.

Or, is this what happened:

Jesus of Nazareth is crucified. He dies. His body is left on the cross for days, as was the Roman custom, to warn any other "King of the Jews" pretender to think twice about stirring up trouble. After a few days have passed and the birds, dogs (Roman crosses were low to the ground), and other carrion ravaged the body, the remains were taken down at night and tossed into an unmarked common grave---a hole in the ground--- with the bodies of other criminals executed that week. The location of this common grave is known only to a few soldiers, as the Romans do not want to give the "King of the Jews" a proper burial nor do they want a known grave to become a national shrine where Jews could later come and pay homage to their "King", possible inciting more trouble. Jesus disciples who were already in hiding, go home to Galilee to take up their prior professions---fishing or collecting taxes. The small band is devastated. Their beloved leader is dead; their hopes of reigning over the New Kingdom on twelve thrones with Jesus are dashed to pieces; there will be no overthrow of the hated Romans after all. All hope seems lost. Then...months or a few years after Jesus' death...a couple of women disciples see a man in the distance, at sunset, and in the silhouette of the fading sun...he looks like Jesus. Is it Jesus? He turns to them, waves with his hand, and then disappears behind a hill. "It was Jesus!" they exclaim. They run and tell the disciples. Soon other disciples are "seeing" Jesus. "He is risen, just as he said he would!" The disciples are thrilled! They WILL reign in the New Kingdom after all! They begin to preach the Gospel of Jesus, telling everyone how he has risen from the dead, as he promised.

...and forty years later, after Jerusalem has been destroyed and most of the disciples are dead, a Greek speaking Christian in Rome writes down the story of Jesus. However, the version of the oral story that this man hears circulating in Rome tells of an empty tomb, the tomb of a member of the Sanhedrin, ...so "Mark" writes down the story. A decade or so later, "Matthew" in another far away location and "Luke" in another, write down the story of Jesus. They borrow heavily from "Mark's" story, from another common source (Q), and from other sources that they do not seem to have shared. For instance, "Matthew's" story contains incredible supernatural tales, such as an earthquake occurring when Jesus died, causing dead people to come back to life...but they don't come out of their graves until three days later! One wonders what they were doing in their tombs for three days!

And two thousand years later, every Christian on earth believes that the stories written by "Matthew, Mark, Luke, and John" are the historically accurate accounts of the life and death of Jesus, when all they are are legendary stories. No one lied. No one made anything up. It's a legend. Now, dear Christian, how many supernatural events such as dead people coming out of their graves and walking around town have you seen in your life? Not many, have you? And how many times have you seen a simple story about a car accident or someone's mysterious death, turn into the wildest tale, with all kinds of miraculous claims, develop in just a matter of days?

So, honestly, friend: Which of the above two stories about Jesus is much more probable to be true?

After Jesus died, his body stopped metabolizing the water

The body does not metabolize water, even when it's alive.

Certainly, it's the answer that the disciples swear up and down is true.

We don't have any disciple's word for that. We have the church's word that the disciples so swore.

And they're willing to go to their deaths for it

For that, too, we have only the church's word.

Yet a first-century audience (that is, an audience which would have been able to call "shenanigans" if the authors were just making things up) believed these accounts, copied them, and spread them both textually and orally throughout the entire Roman Empire and to faraway places like India. . . . This doesn't, by the way, rely on you assuming a priori that the Bible is Scripture and therefore inspired

No, but it does rely on my believing what the church says about the New Testament's provenance.

just that you approach it as you would any other historical text

I believe I'm doing just that, but we may have a semantic issue here. I believe the documents are historical in the sense that they are relics of history. I do not share the church's belief that their authors were attempting to record history.

it's clearly arguing for what were then recent historical events, not telling some long-ago legend.

When I read read the New Testament, I don't find any argument for the proposition "These things really happened." I see narratives about Jesus of Nazareth, but I don't see any serious effort to convince the reader that they are factual narratives.

People today know the difference between fact and fiction.

Actually, a lot of them apparently don't, if the reaction to The Da Vinci Code is any indication.

If you're saying you need more than what is in the Bible to substantiate the supernatural claims, I don't disagree with that. I did not rely on the Bible alone when I converted to Catholicism from atheism.