LT, sounds like you have a great situation there with a nice tree and willing homeowners. Other than the frost mentioned, how stressed was this tree? Was there a lot of deadwood, was the split opening, receding of crown? From the picture you showed, the tree looks pretty nice now.
We recommend mulch rings all the time. And have seen the benefits. A large tree like this in a grass area may have some complications in establishing a mulch ring all the way out to the drip line. (Which I think would look really good.) It is in a slight dip so the mulch, if placed thick enough to deter the grass, may have a tendency to erode back down to the root flare. Also if the mulch was placed thick enough all the way out to the drip line to deter the grass, you would need about 6". Great care would need to be taken in the selection of mulch that it did not create a hydrophobic mat.
Because of this and the fact that most trees do not like major changes all at once, I would suggest starting off with a moderate size mulch ring (say 12 ft dia) and progressively enlarge it.
Unless there is something we don't see from the photos, the tree has come to grips with its location. So I would not recommend bringing in any earth disturbing tools. Let the change develop naturally and slowly as the mulch ring increases in size.
Dave