I think with high impedance headphones, especially 2000 ohms like the HD-424, what they need is sufficient voltage with little requirement for current or power. An amp rated for only 1 watt into 8 ohms would be doing so with 2.83 volts, so all power amps are plenty sufficient. Tube amps will provide plenty of voltage since the phones will play loud with 0.5V and very loud with 1V.
Usually, the two things of concern are damping and impedance interaction. Damping is derives from the relationship of the amp's output impedance to load impedance, and generally one wants the load impedance to be 8 or 10 times the amps output impedance. Impedance interaction is how the load's varying impedance with frequency causes the delivered power to vary with frequency, resulting in an inaccurate frequency response.
Both the above issues are a concern for low impedance phones; high impedance phones makes both issues negligible.
On the choice of taps on the output transformer... I think with 2000 ohm phones all the calculations are going to pretty much approach the same values, so you might try all of them and see if you can hear a preference. When using normal low impedance regular speakers (where power is being transferred) I think one would expect the output transformer to generate more heat with the 4 ohm tap and less with the 16 ohm tap. I don't know, but with the phones I suspect all the taps will present a cool transformer.
