Tough to say. I think I'd put the floor at about 1W for the sake of headroom, but I think the more important factor will be the nature of the power. These things crave current and many headphone amps are not necessarily designed to drive 22ohm loads...especially the OTL amps. Look to a solid state or transformer coupled design that can deliver the goods into 22ohms.
That said, you don't necessarily have to spend a tin to get that. The Magni will drive them in a satisfying fashion. I'm guessing the Asgard will too. The Mjolnir definitely does. The Lyr is not a good option, IMO.
I would expect the Burson to be a nice fit. The Woo 6SE as well.