I haven't, but that curve is indeed familiar to me – it was another possibility that occurred to me while I was doing the initial thinking. I didn't know its usual name, but I re-derived it myself and found that it's what you get if you look at the locus in the complex plane of erf(x+ix) for all real x. It has the nice property that you can get a first-order-smooth transition from a straight line to a curve, by starting at the centre point of the spiral where its curvature is zero. On the other hand, it was less obvious how to find the right segment of one to go between a given pair of points, so my plan was to stick with nice easy involutes for as long as they seemed to be working and move on to more difficult things like that only if they seemed necessary.

Another vague idea I had was to try involutes of things other than circles; in particular, I had an idea that using involute segments of ellipses would add another degree of freedom which might enable me to match up the curvature as well as the direction where two segments met. Again, though, the maths would have been a lot more fiddly (elliptic integrals, yuck), so I held the idea in reserve for use only if it became necessary.