A Sofa King Screwed Unicorn
Short story: I've made a 3D unit! It's Sofa King 3D! The pun is mostly cloudbreaker's fault, but they didn't start it, and I didn't even do most of the modeling, just adapted existing TinkerCAD projects. You can see this unit in 3D, tinker with it yourself, or even download it for 3D printing(I haven't tested the printing yet, so try at your own risk).
Medium story(TinkerCAD description): This is a unicorn with a screwed up horn and screwed up midsection, developed as a fan-made unit for the Side of Sofa King in the Erfworld universe. The pun wrote itself in homage to Erfworld, but I combined Derpy 24/7's Unicorn and DasWonton's Screws for this 3D model of the technically mountable unit, which moves with screwed up actions that wouldn't be particularly comfortable to ride on.
Long story: I designed “A Sofa King Screwed Unicorn” in TinkerCAD by combining and adapting two existing TinkerCAD projects, developed through several projects by several users. Since I was allowed to do so under the Creative Commons license Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0), I am attributing the credit for the vast majority of the 3D modeling to the TinkerCAD users listed below, and wish to update this list if anyone discovers a discrepancy in the chain of creation.
Further, as I am sharing it under the same license as required by use of the license, anyone can share or adapt this design, even for commercial purposes, as long as they attribute credit appropriately and share alike. So, this is available for development into a 3D collectible unit. :) An alternate name to consider, if not limited by TinkerCAD's language filter: Screw Unicorn.
Heh. You're right, Jillian does seem like the horny type.
It might as well screw with the laws of physics and have the flying special; it would fit with my idea that the Screw Unicorn should have high enough move to tempt units to ride it despite the loss to hitpoints, or at least tempt the Sofa King to Sofa-King Order the horror on some Sofa King Luckless unit.