I am not a lawyer, so I must rely on people who are to tell me these things. And they have told me that a state can legally choose which to remain on standard time year round, but they cannot choose which time zone they are in nor can they choose to remain on daylight time year round.
So perhaps you are missing some other laws that govern this? Or perhaps it's a declaration from the Secretary of Transportation that has never been changed?
If you go by what the law says on its face – yes, you need either approval from Congress or the Secretary, and probably the Secretary has made clear they are unlikely to agree to use whatever powers they technically have in this area.
If you start coming up with inventive legal arguments – then it comes down to whether you can convince the courts to accept them. Maybe you will, maybe you won't. But obviously this is a much more legally risky strategy.
Although, at least in this case, it is unlikely that anyone will go to prison if the courts don't like their inventive legal argument. Still, it would require state officials to risk being ruled against by federal court, and some of them might not view the political consequences of that as acceptable.
So perhaps you are missing some other laws that govern this? Or perhaps it's a declaration from the Secretary of Transportation that has never been changed?