We have worked it out in more detail here: Information is Additive but Evolutionary Wait Time is Not.
Note, the example there does not include positive selection. It is a clearly explained math problem. You just get the answer wrong. It is worth understanding what you got wrong.
It will be hard for you to see this with out being willing to see that wait time does not equal 2^FI. That is just false. The example you gave of the 100 safes is a beautiful example of why this is not the case, and it is your example. I’d focus on that new thread if I were you.