Hmm... I honestly don't see it. Isn't enforcing a prayer at the start of a meeting endorsing a religion? Just make all that shit secular. Problem solved.
The tension in the First Amendment with respect to religion lies between two clauses known as the "Establishment Clause" and the "Free Exercise" clause.
The First Amendment:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
[note the "Free Speech" clause follows
outside the bold]
So, as you can see, when one person argues you can't have a town hall prayer due to the Establishment Clause, another stands up and says "well, then you are prohibiting me from freely exercising my religion under the "Free Exercise Clause."
For the most part, the Supreme Court has said that "excessive entanglement" equals a violation of the Establishment Clause."
Conversely, courts have required that governments make "reasonable accommodations" or not "unduly burden" religious practice in order to remain faithful to the Free Exercise clause.
What exactly constitutes an "excessive entanglement" or a "reasonable accommodation" has shifted as public values have shifted. For example, when I was growing up and attending public school in the 60's and mid-70's, it was typical for schools to have Christmas pageants (including having the school choir sing Christmas Carols) and "Easter Egg Hunts." When my kids went through school this would have been an extreme no-no.
As for prayer, courts have found that schools can have rooms set aside before and after school, for example, to allow kids to gather and pray- as a way of making an accommodation. Allowing Muslim women to wear head dress during sporting events is another example.
Personally, however, I don't see how you can more or less open an government meeting with a sectarian prayer without appearing to favor one religion (or any religion). What's more, I can't see why anyone needs to.