Sounds like we might be in the same "old fogie" range, or close, but we don't consider ourselves old fogies!!
We are Canadian, living near Toronto. So we're not American Civil War buffs, but learning the history behind things is always something we love.
We had also wanted to see the Coliseum, the Forum, the Spanish Steps and the Fountain of Trevi. I looked up the places you wanted to pass by and we wouldn't mind doing the same there. They looked really interesting.
As far as the time spent at St. Peters, etc., I
don't want to spend all day there in line ups, etc., then not getting to see anything else. But if we hired a guide, I'm sure they would be able to give us some timing ideas, based on time of year and the fact that we only have 1 day, etc. And I see from the site that we can pre-book these people and they would get advanced tickets for us.
As to shopping, I have to admit I love looking (not necessarily buying) but don't have to do that in Rome, and I doubt there'd be the time in any event.
So, why don't we exchange e-mails and go from email@example.com