I would do this as multiple Surfaces - this looks like an Earth Dam or Berm and you can easily build that with the Create Sideslope Command and then use the lines created by that command to build the surfaces. To compute the volumes I would put a simple alignment (HAL with a fixed height VAL is the best approach) across the site and then se the Corridor Model to add the Surfaces as Surface Instructions. You can then rn Corridor Earthwork Report to get out all of your material Quantities.
I recorded and posted a video for someone else in the last 2 weeks on this specific subject - there issue was a large containment area for an Oil / Gass storage facility that had a complex 3D Subgrade Model and Sideslope did an Awesome Job of that - this would be the same.
Takeoff Module really only has Finished Grade, Subgrades (created from Site Improvements) and Existing Ground +/- Overexcavation. As you say in this case your materials have varying thickness and dont work with a Vertical Sided Site Improvement, so you have to shift approach to create those "complex subgrades" using Sideslope or corridor models. Sideslope is neat because you can create many instructions (like a corridor model) that each create linework for any number of material layers that you can then combine into surface models. The Corridor Model allows you to output all the volumes you want (end section areas method)
Here is a link to the post I made a couple of weeks back
Alan