Thinking about this a bit more. If you want an interpolation compatible offset, reduce the search to a one dimensional problem by fixing the area. This gives a simple rational formula for the length of one control arm as a function of the other. Then pick the value of that to minimize your error metric, for which least squares is probably the easiest to solve. I expect this will give you O(n^5) scaling.

I'll probably implement this, as it's very likely what you want in the variable font case.