When coasting downhill at 70-72mph, I get a severe oscillation in my steering wheel. Applying slight greater braking will lessen it. It does not occur at faster or slower speeds and no pulsation is felt in the brake pedal.
The dealer has machined the front rotors and replaced the pads - even though both were well within acceptable tolerance. This did not lessen the problem.
Check the alignment.
…and have the tires balanced with a Road Force-type wheel balancing machine.
If your dealer does not have this type of equipment, some tire stores have it.
This type of balancing is much more effective if you have tires that are flawed.
Unless you need warranty or recall service I’d not suggest a dealer. There are plenty of good, independent shops that can take care of this car as well as, if not better than a dealer and for less.
What you need right now is a dedicated front end/alignment shop.
Are you saying that this oscillation will only occur at 70-72? As in, it will disappear at 73? Or were you just saying that it starts at around 70 and up?
Brand new h rated tires. balanced and aligned. No vibration due to wheel imbalance at any speed. The shimmy is in the steering wheel only. No sign of any pulsation in the brake pedal - except at 71mph coasting downhill with only a slight braking force applied. Heavier braking will damp it out completely.
Yes, the shimmy only occurs at 70 to 72 mph and only when slight brake force is applied. Heavier braking damps it out completely. The rotors have a TIR of only 0.02mm.
I am under the impression that there is some slop in the rack and pinion or possibly something in the ABS. The Subaru dealer says that the problem is tied to the brakes as this is what the factory tells him.
I am trying to run down other possible causes but so far have not stumbled on to anything.
I can have new rotors installed at my expense for around $300 but since I have already put money into the rotor machining and pad replacement, I don’t think that this will solve the problem.
This is a very odd one since you state that it only occurs during a certain, very narrow speed range. You reference the steering rack slop so that is something that could certainly be considered as a cause. Most of the time any slop is in the innner tie rods and worn Subaru inner tie rods are not a rare thing.
You can check this yourself if you want. Jack one front wheel up at a time, grasp the tire at the 3 and 9 o’clock positions, and try to rock the wheel assembly back and forth. It should be snug. If you can feel noticeable movement then odds are the inner tie rods are worn. It’s also possible that the outer tie rod ends could be loose but the inners are usually what wear the most.
Other possibilities could be a worn ball joint, transmission mount, worn halfshaft, etc. but the inner tie rods are easy to check. They should have been checked during the brake work if this was not done because loose suspension components can mimic brake problems.
Year, make, and model, please!
Since we know it’s a Subaru Outback from the tags, the Model Year will suffice. 
2006,Outback,automatic,2.5,45000 miles.
Your suggestion to check the tie rod ends is a good one. I will do so asap. Unfortunately I will not be able to do it today as I am leaving on a trip, but will do so at the first opportunity.
Right, so you need a front end shop. I think it is completely implausible that it is the brakes. See, e.g. ok’s post below. Someone needs to check everything on the front end.
I have no idea what it means for someone at a dealership to be giving a diagnosis b/c that’s what “the factory” told them. Perhaps they mean there is a technical service bulletin on it? B/c otherwise it doesn’t make any sense whatsoever. Just don’t bother with them.