Went back to the local store to try fitting my road bike into the Model 3. After trying a variety of angles and orientations, I managed to jamb it in there! And jamb is the correct word. It basically involved tilting the frame so the chainrings were high, the saddle low, right in the area where the wheel wells are. Then carefully pushing, which compressed the trunk liner just enough I was able to squeeze it through. It's not ideal, and I don't think there's any way I could do it with the front wheel on. But in a pinch, it can be done. I wonder if the liner could be modified to free up a little more space?
BTW: I was wrong earlier when I said the bike won't fit between the wheel wells of my Prius earlier. It actually does fit, I just don't slide it in lying flat because it's much easier to have the frame tilted up a bit so I can roll it in on the side of the back wheel.