I think we've finally made a decision as to what we'll do with the lawn. Going to add 8-10" topsoil/fill in area depicted and add some erosion type matting. Use small (1-2' high) boulders to outline, then plant some blueberries, perennials, creeping juniper. Top it off with mulch. We'll be careful not to backfill around the trunk of the oak. Total cost $3,000.
The only downside to the above is we don't have the money to fix and re-seed all the other bare and thin patches in the lawn. Will have to wait till Spring. The other option would be to skip the above and fix all of the lawn now including the area around oak, hydroseed and see how well it all takes, especially around the oak. While I understand the oak is partly responsible for the bare area around the tree, I think part of the lower bare area is due more to poor soil, insufficient depth. It's possible if we went ahead with this 2nd option, the area for which we'd have to put mulch and plants maybe much smaller if the new grass were able to "grow in" and establish on the slope.