Well, I got it to work.
Since I can't revolve a helix, I did an approximation of that. I took several points along the ellipse, and I drew a line tangent to the ellipse, and then a line tangent to the ellipse starting at each point. I then drew a lines perpendicular to the tangents, from the points on the ellipse to the axis of my roller. I drew vertical lines off of the point where the perpendicular-tangent lines contacted the axis, and constrained the verticals to the same length as the perpendicular-tangent lines.
Now I have an approximation of the curve I want, defined by the end-points of the vertical lines. I used a spline curve to connect them.
I then radially extruded it. Here's a comparison of this new roller to the old one. The new one is the left half in green, the old one is the right half in red.
I realize, because this is a spline curve, it is only an approximation. However, it is a much closer approximation than an ellipse.
NOTE:
In this example, I happened to make the roller too big for the wheel. Please disregard that fact for the moment. It makes it easier to show the roller in detail, yet still display the entire elipse.