So what would happen if a single juror just remained steadfast that the defendant was innocent despite overwhelming evidence to the contrary? Can a judge remove that juror if they believe they are not being forthright?
From what I understand a juror can only be removed during the jury selection process or if someone outside the jury "tampers" with the jurors. If you get called to jury duty, the quickest way to get out of it is to say you know about jury nullification. But if you don't reveal that and get into the jury you are free to rule as you want and to try to convince the other jurors to do the same.
With jury, you can't blame a single person for the result you didn't like. It was your neighbors that decided. And, at the same time, laws get continuously tested. Every time a jury is called, it's like a small section of society (randomly chosen, and later pruned by criteria) gathering verifying if it still makes sense.
As for the facts. While they are very important, law is also about morality. And while facts remain, morality changes all the time.
And regarding Europe. Some of the sentences handed by judges here, are so horrendous, that I would take american style jury over them any day. Especially when it comes to violent crime.
This is perjury. On your jury duty questionnaire, there was a question (something about "faithfully upholding the law" or something) which is a roundabout way of asking "By the way, you don't plan to do a jury nullification anytime soon, do you?". If you said no to that, then got on a jury, and told everyone to do a jury nullification, you've done perjury, and you actually can be punished for that.
The only legal way to nullify a law is for each member of the jury to individually decide they don't like the law and vote to nullify. You can't convict a jury for falsely acquitting. But you can convict a jury for conspiring to do so.
The situation you describe is known as a hung jury, and would result in a mistrial. Usually this means the case is retried later (with a different jury).
A judge needs cause to remove a juror. This includes a juror refusing to deliberate. In the specific case you bring up, it would be hard to prove that the juror is refusing to deliberate (i.e. "not being forthright") compared to just differently interpreting the facts of the case or the law or disagreeing with how the law should be applied.
It is the purpose of voir dire to weed out jurors with a preexisting bias in the case. You don't want to remove jurors after the case has started, as you run the risk of running out of alternates (there are probably state specific laws on how to handle this without requiring a mistrial though).
Note that this works regardless of which direction the wrong conclusion is in.
People always talk about it in the case of a juror voting to acquit someone when the evidence is that they are guilty but juror choose to disregard it, but historically it often went the other way. There's a long history of black people in the US, especially in the South, being convicted by all white juries that almost certainly would not have convicted on the exact same evidence if the accused has been white.
I don't know if there is a name for this, so I'll call it reverse-nullification, with nullification just referring to the case of acquittal of someone despite the evidence.
Unlike a nullification case, an reverse-nullification case is in theory correctable. A nullification case is not correctable because an acquittal by a jury cannot be reversed by the judge or an appeals court. A judge or appeals court can reverse a conviction so could correct an reverse-nullification case.
However, as a practical matter that often cannot actually be done because often the judge or appeals court cannot tell that it was an reverse-nullification case. A case often comes down to conflicting stories from witnesses with the jury having to decide which witnesses to believe. The conviction may have been an reverse-nullification or it might just have been that the jury found the prosecution witnesses more believable.