a problem with something like the London Pass is that like a cereal box when you shake it, it is full of air and less cereal than you expect.
In order for them to be able to advertise that they cover so many things you MUST be saving money, they pack them with fluff and air - most things are third or fourth or worse tier places that you would ordinarily not consider, at the expense of doing the really important stuff, most of which as mentioned are free anyway.
They can still list places that are otherwise free because they do some little thing for you, like a keyring or a skip the line facility that isn't needed, to entice you to buy the product.
The very fact that you have to rush around to make it "pay" means that you miss the real jewels in the crown.
Now you said that it makes good financial sense for your situation so you must have already done the arithmetic and considered all the above. There is a very small number of folks for whom the London Pass actually makes sense - I am glad that you are in that state.
If you go to the Tower of London in mid afternoon you will be there at peak time and may have to wait in a long queue, maybe over an hour, in the sun on Broad Walk to get into the Crown Jewels.. If you listen to our advice here you can probably walk straight in.
You say "we". How many is we? An even number? There are ways that you can genuinely save money without needing to spend lots of money on a pass.