London Itinerary ?

Thursday I think you are better off prioritizing the three sites and going on your own. The Tower of London gets so busy. I would be there at opening (have done so twice) and take the Yeoman Warder’s tour even if there are a lot of people lined up for it. We went other about 70 people and it was fine, strangely enough! St. Paul’s has an excellent audio/visual self-guide that we enjoyed and the Tower Bridge is easy enough to do. We all thought it fun to walk across on the glass walkway. This would be the day to go to the Sky Garden if you can book it. We ate lunch there and while it was pricey, it ensured we got in! All three sites are a lot for one day, but doable if you take a rest here and there, like a nice long lunch.

We went, at the insistence of our adult son, to the Changing of the Guard and all three of us thought it a tremendous waste of half a day! You have to get there soooo early and stand and then you can hardly hear or see anything of value. Highly skippable, IMO. Westminster Abbey also has a self-guided tour well worth renting. Lines can be long but I seem to recall it was emptier later in the day so maybe look at Rick Steves’ advice in the guidebook about managing crowds. We went once on a guided tour with London Walks at 10 and it was so horribly crowded we bailed half-way through. The second time we self-toured and I think it was later in the day and it was peaceful.

If you're intent on seeing the changing of the guard, look in to St. James Palace (just up the mall from Buckingham Palace). While you won't get to see the full ceremony that takes place in front of Buckingham Palace, you can see detachments of the Old Guard, and bands, assembling and marching (there may also be a way to see some of the guard movements from Wellington Barracks but I've never tried so can't speak to that).

https://www.householddivision.org.uk/changing-the-guard-movements

The above link has more info on troop movements, where they assemble, where they march, etc. So again, while you don't see the full ceremony at Buckingham Palace (which, to be honest and as has been mentioned, can be nearly impossible to see anyways with all the crowds assembled around it unless you get there well in advance and dedicate your morning to it), a lot of people miss out on the chance to more easily see the the Old Guard as they move from one palace to the other, in full uniform, with bands, etc.

St. James palace also has sentries stationed there that you can get pictures near, often without having to complete with crowds of others trying to get photos (I say "near" and not "with" as you don't want to try standing too close to or behind them).

Even perhaps checking the Horse Guards schedule and movement could be worthwhile.

It was a private guide that took us to St. James instead of Buckingham Palace for the changing of the guard, and I was extremely glad he did. I do believe Rick Steves' London guidebook mentions St. James Palace as a good place to see the changing of the guard also, though.