Your writing is not very clear. when did you get the permit? It sounds like it is no longer valid. As Mike told you, it doesn't matter what the permit people do or say. Get a J license. It's a priority now. If you are given a rental car anyway, and you get stopped for any reason by police, you will be in deep trouble.
If you are British, it's a very simple matter, no testing required. Go.
By the way, if you want to rent for just a day, can't your wife drive?