Your geographical organization looks good to me. For extra assurance, you could ask Google Maps to plot walking routes from point to point. Watch for places where the route is circuitous (indicating care must be taken to avoid a hill or a pay-to-enter archaeological area) or where the walking time is more than the standard of 20 minutes per mile. The latter would suggest there's some hill- or stair-climbing involved. The Capitoline Museums are at the top of a significant set of stairs, for example.
I assume you have already taken care of tickets for the tours mentioned in your original post, including the Domus Aurea.
I'm always dead to the world on arrival day and wouldn't plan to do anything beyond aimless wandering around outdoors, because I wouldn't remember doing it. If you are lucky enough to survive the overnight flight well, I think you could include the Jewish Ghetto on your arrival day.
Day 2 looks heavy to me in terms of getting everything accomplished and needing to be on your feet a lot. The Capitoline Museums are in two buildings connected via an underground display area. I'd urge you to poke around on the website and prioritize the areas you most want to see so you don't miss what's most important to you if you begin to flag. I'll mention here that the Jewish Ghetto isn't far from the Capitoline Museums, but it's in the opposite direction from Monti, so I don't think you'd want to try to fit it in on this day.
On your Vatican/Trastevere day, try to see Santa Cecilia as well as Santa Maria in Trastevere.
Not too far from St. Peter in Chains is the aforementioned Santa Maria Maggiore. In that general area are two quite small (thus quick to see) churches with stupendous early mosaics; put a 1-euro coin in any light meter you notice for the best view. During my February visit, St. Praxedes was open from 10 AM till noon and from 4 PM to 6 PM--I think daily. Santa Pudentiana was only open 9 AM till 11:30 AM Monday-Saturday.
San Clemente is quite interesting. It now requires a ticket purchased in advance. The afternoon time slots, at least, were not selling out way in advance in February, but you cannot purchase an entry ticket onsite. It's easy to do online.
I can't really speak up for Castel Sant'Angelo, because I didn't have time to see it myself. It's not often mentioned here, and that is probably for a reason. However, it supposedly has a good collection of paintsings, sculpture and military memorabilia, and it sometimes houses temporary exhibitions.