Pennylane...thanks for the explanation. Of course, I guess it does make sense that there has to be documentation of a legitmate religious "excuse" for the exemption.
At first, I thought the suggestion for a lawyer was a huge overreaction, but after reading the OPs latest post, I see that the consequences to this student are so significant that maybe one is warranted anyway.
OP....that being said, I DO think the ACT is your only solution to your immediate issue. Your son's stats are higher than my son's. After trying the SAT twice, I signed him up for the ACT and only gave him a few days notice. I didn't tell him anything about the test and told him not to worry about preparing. He literally did not know a single thing about the ACT (we're on the west coast--no one out here takes that test). Long story short--he did better on the ACT (significantly better on the math) than the SAT. After he saw the results, he did a one practice test from the book to get the timing down and took it a second time. Long story short: his 2nd ACT score was better in all subjects than his SAT score--so much so that he didn't send SAT scores to any of his schools.
In my opinion (I've studied both tests in great detail now), the timing is just not going to be a big issue for your son. It can't hurt to at least have him try it.