The thing is, my reasoning doesn't actually depend on the horcrux realization, tough I give it better than even odds they knew that long before he even got the Hogwarts letter. Like, some time around the bitten math teacher or the science fair incident.

The cloak is the obvious counter to the mirror. Using it isn't some super-obscure piece of lore. The mirror has power over things reflected, the cloak removes you from that category. Put yourself in Dumbledores shoes as you are packaging up that thing after spending oceans of time and effort setting up the mirror.

Just No. This is not a plausible mistake. I'm shocked and a bit dubious Voldemort is buying it, but he does think everyone is a complete idiot, so...

If Dumbledore didn't want the cloak to be used against the mirror it would be stashed someplace very obscure. Or if he was feeling smartass, in the mirror itself. Handing it over to Harry was a deliberate move to put it into play.