The cited Reg says "within the time prescribed by law (including extensions) for filing the return for such taxable year".   To me, that means by April 15th/October 15th.

Just because you didn't have any issues doesn't mean it is correct.

Unfortunately, I've seen a number of questionable items in the Master Tax Guide.  Does it say that for an AMENDED return?  It is allowed for a late original return.

I would be happy to be wrong, but to me everything says that if it is on an amended return it needs to be done by April 15th/October 15th.