Due to the angled surfaces at each end, I wasn’t able to use a straight extrusion process. I started with the cross-section you had and then rotated it 90 degrees. The rotated copy was scaled to fit the angled circles at top and bottom. Then I created about twenty cross-sections and scaled them each in x and y to connect with the four side profiles (each of which is different, of course). Then I could have connected the horizontal profiles manually, but I used Fredo’s Curviloft to create splines between the sections. The last step was to put the first shape into a group and then create a copy vertical which was then rotated 90 degrees counterclockwise. Using the crossing lines at each end, I used the front view to align one set by rotating and then the same in the side view for a second rotation. Then I repeated for a third section rotated 180 degrees and then a fourth section rotated 270 degrees (-90 from original position). The result is not quite what I expected … it seems to spiral gradually away from the origin.
BTW, I should have made the first shape a component before moving and aligning the next ones. I needlessly used separate groups for everything.
[edited] It’s late … that’s when I make mistakes. I used a component, after all, but not for the group of four components.
[add later] One more picture: