Ok, so the advance to next week became grayed out in my new save instantly after I took the family out for the weekend, so I'm thinking it's actually a bug now and not the save file.
You found a real one — and this one was my fault, not your save's. When you finish a show and hit "Back to Garage," the game was switching screens but forgetting to clear the show result behind the scenes. A safeguard I'd just added (graying out Advance Week on the results screen so people don't skip a week by accident) was then reading that leftover result and locking the button forever — and a refresh couldn't clear it. The Family Saturday timing threw us both off; the real trigger was a show you'd done earlier.
Good news: it's fixed, and the fix also cleans up already-broken saves automatically — so your backed-up file should load and work again once the new build is up. You don't need to start over. Thanks (genuinely) for the repro steps and the save file offer — "grayed out instantly after X" is exactly the kind of detail that makes these fast to squash. You've got a real knack for bug reports. 🍺