OK I've dealt with this by fixing all the points that can be fixed (checking both the x and y domain) and issuing a warning if there are any points where we can't do anything. In real-world scenarios it is likely that there will only be one or two of such points, and they will lie on a boundary. I think this is an acceptable compromise in order to gain the generality of transforming to and from any projection.

Unless you have a better idea...