How do evangelical universalists reconcile their position with the designation for Judas that it would be better if he had never been born? By "evangelical" in this context I am referring to those with the common evangelical view that the Bible is the word of God and inerrant in the autographs. 

The idea that Judas might be ultimately saved would be required to hold to universalism, but it seems irreconcilable with the idea that he would be saved and yet be one of whom woe is pronounced and that it would be better for him not to have been born. (Matthew 26:24, Mark 14:21)
I identify as an evangelical universalist. I don't know if you'll find this worthwhile, but here's my take. 

It sounds an awful lot like a figure of speech to me. If it is, it's best not to draw too many conclusions based on it. (Bart Ehrman left the faith because the mustard seed isn't really the smallest of all seeds.)

In support of the figure of speech reading, I'd point first to a general pattern in Christ (I assume we don't need a list to agree that Jesus used fos's quite a lot), and I'd point second to the fact that we don't even have to go outside the Bible to see a similar occasion of language predating Christ's usage here. It's in Ecclesiastes:


  Eccl. 6:3 A man may have a hundred children and live many years; yet no matter how long he lives, if he cannot enjoy his prosperity and does not receive proper burial, I say that a stillborn child is better off than he (my emphasis).


Here we see language similar to Christ's ("a stillborn child is better off") to describe someone who "cannot enjoy his prosperity." This last seems a particularly interesting piece of language when applied to Judas, whose prosperity was the field in which he died. 

It gets even more interesting after that:


  4 [the stillborn baby] comes without meaning, it departs in darkness, and in darkness its name is shrouded.
  5 Though it never saw the sun or knew anything, it has more rest than does that man—


So verse 5 indicates in what way it's better not to be born--"it has more rest."

Then comes v. 6:


  6 even if he [the man who can't enjoy his prosperity] lives a thousand years twice over but fails to enjoy his prosperity.


And then comes the end of v. 6, where, especially if this passage is Jesus's referent (as it seems to be) things get intensely interesting. I kind of want a drumroll for this, so play one in your mind before you read:


  "Do not all go to the same place?"


That's the end of v. 6. Interesting, huh? :)