How to replace solid face with surface face?

My understanding of the problem is that you want to use the surface you created as the top surface of your solid. I would have started my model a little differently but with what you have here is how I would achieve what you are looking for.
Here is a link to video of me doing it.
These commands are not on the standard feature ribbon by default and you can add them if you use them a lot, or do like I did and just use the command finder search bar.

  1. Step 1:

    Move the cutting surface to where you want it.

  2. Step 2:

    Use the surface to cut the solid into multiple bodies.

  3. Step 3:

    You can choose to consume the bodies you don't want during the cutting procedure or delete them later if needed.