Carlmm and cruisemom42, you have both been most helpful! I checked coopculture for Domus Aurea tickets for our dates, mid October. The dates we will be in Rome were in grey, which I hope means they haven't been released to the public yet. I would like to avoid buying tickets from a tour company.
I like your idea, cruisemom42, of taking a bus to the furthest point on the Appian Way. It would save some backtracking if we started from the visitor center. I've looked at the park website and will have to study it some more. Unfortunately, my Rick Steves's book fell to pieces after our last trip. I'll check the bus routes; I was thinking taxi from where we're staying in the Pantheon area, but a taxi would certainly be cheaper.