A skirt over leggings ok?

Should be fine. It's exposed flesh that's the problem.

As long as your knees are covered (not showing) you are good, so I see no reason your attire won't work.

Museums= anything goes. Churches= cover naked shoulders, don't wear excessively short skirts. Just above knees should be ok.
Buy a scarf (plenty of cheap ones in Italy). Cover yourself with it at the entrance if you are in appropriately dressed, and take it off once you pass the checkpoint. Many years ago my wife and I were in Rome, it was hot and my wife had a miniskirt. We were at the Vatican and she couldn't possibly get in with that. A former high school friend of mine, who lived in Rome, gave her his business suit jacket, that she tied around her waist. That was good enough. As soon as we passed the checkpoint she gave the jacket back to my friend and she toured St.Peter's basilica with her miniskirt. Although there are rules, however you are in Italy, and rules in Italy are interpreted, let's put it this way, "liberally".

Terry, if you take a scarf with you (for shoulders, unless it can double as a wrap skirt), you will avoid being given a temporary cover-up, which is not exactly a fashion statement.

I would say that the rules in Italy are enforced inconsistently, not liberally. I've seen church guards be either extreme - absolutely inflexible or clearly uninterested.

Thanks to all for your info. I think my plan should work just fine!