Problem: Accounts of Judas' death conflict (in many ways)

The two accounts of the death of Judas Iscariot seem directly contradictory. Here's Matthew 27:5:

And throwing down the pieces of silver into the temple, he departed, and he went and hanged himself. (ESV)

Now this man acquired a field with the reward of his wickedness, and falling headlong he burst open in the middle and all his bowels gushed out. (ESV)

There are many problems in harmonising these verses. First, the most obvious: did Judas hang himself, or fall?

The simple reading of Acts is that Judas just fell, and died as a result. But that would be a rather bizarre event. By combining the accounts in Matthew and Acts, things actually make more sense: Judas hung himself and the corpse later fell and burst open. So on this point the two accounts actually fit together quite well.

But what about the silver?

Did he throw the silver away or use it to buy a field? This is as blatant as contradictions come.

A reader of this page notes that Matthew 27:6-8 has the priests of the temple buy a field with the money, and suggests that this means, by extension, that Judas "acquired the field". This is also the view of the NIV Study Bible:

Judas bought the field indirectly: the money he returned to the priests (Mt 27:3) was used to purchase the potter's field (Mt 27:7)

The ESV Study Bible says the same. But I find it hard to believe that any competent author would write in such an obscure way, stretching the meanings of words beyond recognition. The real meaning of Acts is clear as day: Judas bought the field himself.

Why is it called the Field of Blood?

In Matthew's account, the "blood money" that Judas returned to the priests was used to buy a field which was later used to bury foreigners. For this reason it became known as the Field of Blood. (Note that there's nothing in Matthew to indicate that Judas went to the field.) This is Matthew 27:6-8:

But the chief priests, taking the pieces of silver, said, "It is not lawful to put them into the treasury, since it is blood money." So they took counsel and bought with them the potter's field as a burial place for strangers. Therefore that field has been called the Field of Blood to this day. (ESV)

But Acts 1:18-19 tells us that it was so-called simply because this was where Judas fell and his bowels gushed out.

Why was Judas in the field?

Finally, why was Judas in the field? Under the natural reading of Acts, Judas was in the field because he had purchased it. But if Matthew is correct, this can't be the reason, since he didn't really purchase it.

Combining it all... a solution?

Tektonics makes a valiant effort to combine everything Matthew and Acts say on the matter, and we end up with an account that looks like this:

Judas returns the silver.
Judas goes to a field.
Judas hangs himself.
And then the corpse falls on the field.
Because the field is now defiled, the priests buy it to bury foreigners in.
Since they bought it with Judas' money, in a sense he "acquires the field".
Because of all of the above events, it becomes known as the Field of Blood.

While this almost explains everything, it leads to the absurd result that Judas acquired the field after he was dead! This is, of course, not what Acts says. The sensible reading of Acts is that, while still alive, Judas bought a field, and then he died in it. The above timeline is therefore ruled out.

If you accept the idea that Judas "acquired the field" when the priests bought it, I think you have to say that this happened before Judas died. He then went to that field to hang himself in.