However, if people usually aren't arrested for yelling at 3am, and it's only because you are yelling out Bible verses that you were arrested, then arresting you would be unconstitutional.
As another example, some religions require that members wear headgear. See http://en.wikipedia.org/wiki/Kippah#Kippot_in_secular_law for some of the laws regarding the wearing of yarmulke. In general, if a religious use is not singled out and there's no good safety or security reason to ban headgear, then it cannot be banned.
Consider also one of the court cases I once read, about a lawyer who was also a priest. He wanted to wear his clerical clothing while in the courtroom. The judge refused it, on the grounds that it may unduly sway the jury. This decision was appealed and upheld, as I recall.
Like I say, these decisions are often a matter of tension between different needs.
So let's look at the copyright issue again. The copyright law does not place extra copyright restrictions on religious practice. Thus, it is not directly abridging the free exercise of religion. Still, as you point out, it can incidentally place some restrictions on religious practices. But as I pointed out, the law specifically grants religious services extra freedoms that the general public do not have, so you would have to show that there is still a serious restriction.
Suppose your specific case were taken to court. The judge would look to understand the tensions involved: is your ability to practice your religion being abridged by the prohibition of using copyrighted material outside of religious services? How serious is that abridgement? What acceptable alternatives exist?
For example, if you were in the Church of Irving Berlin, with 400 other members, then you would likely have a stronger case than if you were one of the three remaining Shakers, whose religious practices haven't changed much in the last century. (And that's why I asked about your religion, because it does have bearing to the question.)
You say that it's "spiritually meaningful" to you. However, there are any number of things which can be "spiritually meaningful", many of which run afoul of the law. "Spiritually meaningful" by itself cannot be a good guideline.
As an interesting, if only somewhat relevant example, one of the Five Articles of Faith that baptized Sikhs are supposed to have with them at all times is a kirpan; a short dagger. Sikhs follow a warrior faith, and are charged to defend the oppressed and persecuted. But wearing a dagger is illegal in some places. See http://en.wikipedia.org/wiki/Kirpan#Legality for details.
If you can convince others to join in your faith, where the faith requires you to violate copyright law, then perhaps you can get some legal judgment. But as a single member of the faith you're not going to get a favorable judgment given the reasons you listed. Again, the tension is that people can have many different sorts of spiritually meaningful beliefs. Someone may truly believe that it's best to go around at 3am to wake people up, as a way to spread knowledge of their faith.
Do we allow all aspects of all faith to trump all laws? That makes no sense.
> "Has anyone ever raised a constitutional argument for any use of a copyrighted work outside of the scope you have mentioned"
I don't know the this (or really any) area law. A quick search finds http://en.wikipedia.org/wiki/Christian_Copyright_Licensing_I... and http://www.christiancopyrightsolutions.com/factsheets/ .
The latter includes http://www.christiancopyrightsolutions.com/docs/factsheets/F...
> Myth #3: “The religious service exemption allows me to broadcast my church’s performances.” ... This was a real grey area until 2006, when a publisher named Simpleville took a radio station to court for rebroadcasting several church’s’ services, including the music portion. ... The court rejected the argument, stating that the exemption applies only to performances that occur at the place of worship; it does not extend to broadcasts of those performances.
The court decision is at http://www.leagle.com/decision/20061744451FSupp2d1293_11642 .
> the exemption does "not extend to religious broadcasts or other transmissions to the public at large, even where the transmissions were sent from the place of worship." H. Rep. No. 94-1476, at 84, reprinted in 1976 U.S.C.C.A.N. at 5698-99.
I think that settles your question for you.
You ask: Is it completely beyond reason that someone could argue that the internet is their "place of worship"?
Not at all. But when you say "the internet" do you mean a public webcast that anyone can receive, or do you mean a place where members of the faith can get together? These are quite different things.
If it's the latter, then I think you can make a good case that it's a place of worship.
However, if it's broadcast to the entire world via the internet, then there's little difference between that and broadcasting it over the airwaves, is there? I mean, while the technology of the internet is only a few decades old, the idea of broadcasts have been around for a century, and the law has long ago adapted to that.
Consider also that publishing books and pamphlets are other forms of broadcast. The New International Version translation of the Bible is under copyright by Biblica, Inc. Many people use it as their Holy Book. Many people believe that proselytizing is also part of that faith. That doesn't mean they can violate copyright by making unlicensed copies of the NIV in order to encourage others to join their faith.