I am not sure what I am suggesting is the best solution but give it a try if no better option is proposed here.
1. Go to Direct Editing mode
2. Create Face Group (NOT Generate...) > approximately select one side using mesh selection tools.
3. Repeat above for two other sides
4. Finish Direct Edit
5. Separate mesh body with All Face Groups type
6. Hide unwanted bodies
7. For each of separated sides repeatedly apply Remesh and/or Reduce with lowest fidelity settings. With a bit of luck you will end up with a planar surface with only few mesh vertices. If some vertices remained out of plane you can go to Direct edit and delete them (but you probably don't need with the mesh I see in your picture). This step acts as an averaging. Though not sure how close is this to best fitting mathematically.
8. Convert each mesh body to BRep. For this purpose faceted conversion is enough. You can use one of the faceted faces for defining a plane.
I've made a screencast using a mesh I generated to compare the plane with the original body's surface. In my screencast I went a bit further and converted it prismatically which gave a me a completely flat surface.
Hamid