My first attempt at a new process of writing melodies has produced something useful, in part...
What I ended up doing was working out my chord progression, then playing on the piano and singing possible melodies. What was surprising to me was how easy it was to come up with good melodic lines this way.
Now, the melody that I'm working with does still need some work (I'm using it in a song, and therefore needs more variety), but I'm quite pleased with how this process works and will be using it more often and that is something that I'm quite happy about.