Have you come across Raph Levien's work on font design? He likes to use sections of an Euler spiral, which feels to me not a million miles away from your approach. (Fewer degrees of freedom per stretch of curve, etc.)

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.

Having now had a preliminary look at Levien's thesis, I see what you mean – several paragraphs in it could easily have been paraphrases of things in the above entry (or vice versa). He's taken the maths a lot further (and not been as scared as I was of solving complicated numerical problems), and he's got a much wider overview of the various problems that need balancing against each other (whereas all I saw was the one problem that had been getting in my way, and just solved that), but in spite of all that there are indeed recognisable similarities in attitude.

One notable difference in methodology between us is that he seems to like to draw his font outline the same way the eventual format specifies it, i.e. outlining the filled area so that you have to trace along both edges of a stroke. One of my first decisions was to avoid that (except, as usual, in cases where it turned out to be the right thing after all :-) in favour of using a single curve to define the centre line of the stroke and then separately specifying a varying nib. Doing it my way, it's easy to draw crossing lines (such as in the treble clef) and be confident that the portions of a stroke on each side of the other will line up as if they were two parts of the same sensible-looking curve, because they are. Doing it his way, you have to get that right by eye. Also, even in the absence of crossing strokes, I found it difficult to draw two nearly-parallel curves in a way that made them vary from parallelness just right with respect to each other.

Then again, I've looked at some of his actual font designs, and they seem to have stroke widths which vary more subtly than mine in a way that looks deliberate, so it seems entirely plausible to me that his method is better suited to his level of skill while mine is better suited to mine!

Still, all very impressive, and I'll probably finish reading his thesis at some point in the near future. Just a shame he decided to apply for patents.