On Holy Trinity Church v US:
That's a really odd stance to take on your part, particularly as this case has been loudly denounced by Justice Scalia as inviting "judicial lawmaking." The case was explicitly made on the intent of the law, after all, and not the text of the law, in direct contradiction to your claim that they were basing their decision off the constitution. Your claim becomes particularly specious when it doesn't look like this case even ruled on the constitution, but instead on a law barring foreign workers. The establishment clause doesn't appear to have been touched on.
On Vidal v Girard Executors:
I don't see how this supports your case. The court upheld the statute in Girard's will to prevent the teaching of any religious doctrine in the schooll to be built on his trust, because the will did not explicitly expunge Christianity, but all religion. This seems in perfect keeping with later court decisions on the constitutionality of religious issues.
On Davis v Beason:
Ugh. This decision sounds like a particularly ugly infraction of the first amendment, because they upheld a law specifically designed to disenfranchise Mormons. I'd fully support the law, mind you, if it only required that people don't practice polygamy to vote (as polygamy is pretty odious). But it also required that they don't belong to an institution that supports polygamy. So I'd just have to say that this case seems to me to be completely out of bounds, and very much against the free exercise clause. Either way, though, this case was about the free exercise clause and not the establishment clause, so I don't see how it applies.
On Reynolds v US:
Since this is a ruling on the free exercise clause and not the establishment clause, I don't see how it applies to your claims.