London Pass with Oyster Travelcard?

You're smart to pass on the Visitor Oyster Card. Just buy a regular Oyster card when you arrive in London.

If you actually visit the places on that list with your London Pass, then you'll get your money's worth. And only you know how likely it is that you will.

However, you will still deal with queues.

The LP will give you "fast track" entry (whatever that means) only to St. Paul's and Hampton Court Palace, of the attractions on your list. And the LP page listing the handful of "fast track" venues, also notes that queues for security checks may occur. AFAIK the LP doesn't allow you to cut to the head of a security checkpoint line. So if it were me, I wouldn't expect to "skip lines" because of having the LP.

About Hampton Court Palace. I went there a few years ago, on a weekday morning. I took a train - the station is a short walk from the HCP entrance. I got there not long after opening, and there was absolutely no line to buy a ticket. What there was, was a LOT of walking to do. I loved the place and want to visit it again. It's amazing and fascinating - and the buildings and grounds are enormous. I don't know if they have instituted security checks at HCP since I was there; I know they didn't have one when I visited.

In general, the London Pass doesn't work well for shorter periods. A solo traveler, buying a London pass at a discount, for a longer period of time tends to do the best.

With such a short time in London, I'd consider skipping a day trip to the Cotswolds. Most of the expensive attractions that the London Pass covers are half day visits, such as Westminster Abbey, Tower of London, and St Paul's Cathedral. A plan that has worked for me is to visit an expensive paid attraction in the morning and then visit a free museum in the afternoon. For example, a morning at Westminster Abbey, followed by lunch and then the afternoon at the National Gallery. I love the theatre, so that is often the plan at night, although the museums have at least one late night every week, so that's another option.

I've never heard of London Pass getting theatre discounts, but they very well may have some sort of discount code to use. I'd suggest using the TKTS booth in Leicester Square. There's a pub right there and he can have a drink (doesn't have to be alcoholic, they have soft drinks as well as coffee and tea) while you wait in the TKTS line. You can buy tickets for 3 days out, so if you're wanting to see a couple of shows, that can be accomplished with just one visit.

I'm not a fan of the Hop on Hop off bus as I feel you waste too much time sitting in traffic looking at bank buildings while you're waiting to drive by the next site. There's nothing like being out on the water with the Thames cruise on a glorious sunny day, but of course, they're weather dependent. I'd think it would be miserable in rain and probably not worth the money if it is grey, cloudy and damp.

So, all in all, I don't think the London Pass will be a good value for you. And, certainly don't get it with the travel option. Just get an oyster card and use it as pay as you go. If you end up with a lot of coins, you can use 10p and up coins to top off the Oyster card as long as there isn't a line behind you.

Note that for some of your "must dos" and "could dos," you can get cheaper tickets by booking ahead online. In my non-comprehensive research, I found:

Tower of London £22.70 online / £26.80 in person
Westminster Abbey £20 online / £22 in person
St. Paul's Cathedral £16 online / £18 in person
Kew Gardens £16 online / £17 in person

and some "biggies" you didn't mention:
Churchill War Rooms £18.90 online / £21 in person
Kensington Palace £19.50 before 13:45 / £16 after 14:00
Royal Observatory Greenwich & Cutty Sark £15.65 online / £20 in person
Tower of London £22.70 online / £26.80 in person