Hi simba, I've attached the result of one covering method here.

First I had to rotate your objects so that their edges ended all one the same flat plane.

Then I deleted the end caps and used Edit > Trim with the "Add trim points" option on each edge to split it into 3 pieces.


Then in each corner area I used Construct > Blend between 2 neighboring edges to build these pieces:



Then the remaining opening was filled in with Construct > NSided:




The result of that construction is in the attached 3DM file.

- Michael