I brought up three situations, and then realized there weren't any factors I could weight for a heuristic. So I made them up, starting from a list I already had on factors that go into estimating software projects.
In the process, I've also made the attempt to list every commonly used software methodology and/or process framework. I'm certain I've missed some (such as ICONIX) but at least this is a good start.
Different people made different recommendations. The reasons why they made them was at least as interesting as the decisions they made.

I've also found a couple of books, notably Balancing Agility and Discipline which deals explicitly with people who are on the fence when it comes to software methodologies. I'll come back and update this post as I get a better picture.