It's a bit difficult to decide what the rotational speed needs to be limited to to be effective. Assuming it is in the region of 30 rpm and that may be too fast, I think it would be a reasonable point to start with about 20 magnets.
You will have to determine the most effective damping arrangement, it may be a copper disc fixed to the fixed steel plate with perhaps 1/4" air gap or it might be more effective to slot the disc and cast aluminium in, like a flat squirrel cage rotor.

Brilliant.

Drag forces go up linearly with the speed of the motion, which is EXACTLY what you want to damp out an oscilation.

How much 'braking effect' can I expect from this, and how many magnets will I need to use at what size disc to brake the rotation sufficiently to reduce the chance of damage in turbulent winds ?

You can expect an ENORMOUS braking effect even from moderately small magnets.  I'd be surprised if more than a single pair was needed.  Pretend the region of the copper between the magnets is one coil of a genny and it's dead-shorted.

= = = =

I'd like to suggest an alternative geometry:

 - A vertical cylinder - basically, a hunk of copper pipe - around the central support.  Mount with standoffs at two heights to make it solid and provide clearance near the center.

 - A pair of magnets mounted on a piece of iron mounted to the bottom of the mill, hovering over the end of the copper pipe.  (Imagine aa pair of pliers about to grab it.)

The idea here is that dirt and water will tend to fall off rather than accumulate and foul the rotation, eventually freezing the mill in a particular position, or promoting corrosion of the parts.  (You'll still want to shroud the top if you're in a place where it gets really cold, so you don't have rime ice form some day and jam it anyhow.)

The opposed pair of magnets means the field is nearly uniform between then so the cylinder doesn't have to be perfectly straight and centered to get a constant drag.

To minimize the sideward load and wear on the central bearing, put the magnets at the same orientation from the axis as the normal (non-furled) orientation of the tail.

You can adjust the spacing of the magnets to adjust your drag.  (Mount them on bolts and use locknuts to fix them where you want them?).  You want it to be damped just enough that it doesn't wig-wag, because damping also slows furling.  (It should be about 10% underdamped for best wind tracking.  If it initially overshoots just a tad on a sudden wind change, you've got it.  "Critical damping", i.e. the minimum damping that gives you no overshoot, loses more from the delay in following the wind change than a slight overshoot loses by going too far.)

It would be difficult to speculate about the "Best" amount of damping I think - although I'd think 8 of these, running close to a thick copper disk would probably do quite a bit (guessing), although perhaps not for a 16' machine.

I think another big factor is the rotational weight of the alternator, and the hub (and the blades, although its the forces on the blades you want to avoid.  Just watching mine, and Matts larger machines we've made - they seem to move pretty slowly, even in gusty conditions.  I think it has to do with the weight of the rotating parts, mostly in the alternator and in the blade hub.  It would be fun to experiment... if it seems to be yawing too fast, with simply making the blade hub heavier.  Of course it'd  start a bit slower but it should balance out in the end.

If your machine is yawing a lot,
you might even use the yawing
brake disk as a heating system?
The disk will become warm while
it is braking.

Or you might put some coils there,
to get some usable power from
that disk, too...