Ask at the gate: "Hi, I'm a displaced premium-cabin traveler, can you please double-check that I'm on the departure-management waitlist for the first-class cabin?". If they say "no, you're on an H fare, not a displaced premium-cabin passenger" then you can ask them to take a look at your e-ticket. Totally crazy that this stuff is necessary…

Did anyone get an upgrade? If yes and it wasn't it you, it sounds like you could talk UA into paying you a refund for the price difference between "A" and "H" or perhaps "A" and the cheapest available coach fare at time of purchase.